If Jesus is not God according to Jehovah’s Witnesses, why was He accused of blasphemy?

The question contains an incorrect premise. Blasphemy is a vague charge, and only in the extreme form would stoning someone to death for blasphemy involve someone claiming to be God.

To blaspheme is to speak with contempt about God or to be defiantly irreverent. Blasphemy is verbal or written reproach of God’s name, character, work, or attributes.
https://www.gotquestions.org/blasphemy-blaspheme.html

Jehovah's Witnesses follow a similar understanding in so far as understanding blasphemy to be a vague charge.

Blasphemy includes the act of claiming the attributes or prerogatives of God, or ascribing these to another person or thing. (Compare Ac 12:21, 22.) The Jewish religious leaders accused Christ Jesus of blasphemy because he said that the sins of certain persons were forgiven (Mt 9:2, 3; Mr 2:5-7; Lu 5:20, 21), and they tried to stone him as a blasphemer because of his declaring himself to be God’s Son. (Joh 10:33-36)
https://wol.jw.org/en/wol/d/r1/lp-e/1200000769

To ancient Jews, anyone claiming to be God would be making a category error - a human cannot be God, who is Spirit. (Indeed, Jesus says the same thing - John 4:24, "God is Spirit." Funny that.)

For a JW source, see Worship God “in Spirit”.

You might as well ask "If St. Stephen wasn't claiming Jesus is God, why was he accused of blasphemy?" Nowhere does anyone say St. Stephen is claiming Jesus is God. Yet he's still accused of blasphemy (Acts 6:11-14) and stoned to death after being tried for blasphemy (Acts 7:51-58).

Jesus was accused of blasphemy by the Jews because they wrongly leaped to the conclusion that saying “I am the Son of God” was the same as saying “I am God”.

How did Jesus respond to this erroneous point of view?

The Catholic Jerusalem Bible reads: “

Jesus said to them, ‘I have done many good works for you to see, works from my Father; for which of these are you stoning me?’ The Jews answered him, ‘We are not stoning you for doing a good work but for blasphemy: you are only a man and you claim to be God’. Jesus answered: ‘Is it not written in your Law: I said, you are gods? So the Law uses the word gods of those to whom the word of God was addressed, and scripture cannot be rejected. Yet you say to someone the Father has consecrated and sent into the world, “You are blaspheming”, because he says, “I am the Son of God”. If I am not doing my Father’s work, there is no need to believe me; but if I am doing it, then even if you refuse to believe in me, at least believe in the work I do; then you will know for sure that the Father is in me and I am in the Father’” —John 10:32-38.

These Jews evidently jumped to the conclusion that Jesus was making himself God because Jesus attributed to himself powers that the Jews believed belonged only to the Father.

Jesus had previously said that he would give “eternal life” to the “sheep.” The Jews knew no human could do that. But they were overlooking that Jesus acknowledged having received everything from his Father, and that the fine works he was doing proved that he was his Father’s representative.

When questioned before the Sanhedrin, Jesus was falsely accused of blasphemy, not because of claiming to be ‘God the Son,’ but because of claiming to be the ‘Messiah, the Son of the living God.’ (Matt. 26:63-68; Luke 22:66-71)

John 5:18

The Jews began seeking all the more to kill him, because not only was he breaking the Sabbath but he was also calling God his own Father, making himself equal to God.”

Jesus hadn’t said he was God. He called ‘God his Father.’ The Jews objected to his claiming this relationship to his Father, this special Sonship.

And just as they were wrong in labeling Jesus as a Sabbath breaker, they were also wrong in their assertion about Jesus’ making himself equal to God because of ‘calling God his own Father.’

Jehovahs Witnesses would most like interpret him being only the Son of God and not God the Son as well

Matthew 26:63-64 -- The high priest said to him, “I charge you under oath by the living God: Tell us if you are the Messiah, the Son of God.” “You have said so,” Jesus replied. “But I say to all of you: From now on you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.”

Since they do not believe Jesus is Divine, they interpret these verses as Him claiming to be the Messiah and that the Messiah is not God Himself.

I hope this helps and makes sense to you.

The Jehovah's Witnesses have published in their literature their explanation - that the religious leaders who accused him of trying to make himself God misunderstood. In their New World Translation of John 10:33, they have those leaders saying, “because you, although being a man, make yourself a god.” This is also in their 2006 book, The Greatest Man Who Ever Lived, section 81, giving the JW explanation as to why there were further attempts to kill Jesus. After quoting that verse, the book asks,

“Since Jesus never claimed to be a god, why do the Jews say this?”

JWs say that Jesus was not God, but “a god”, and have rendered John 1:1 that way too. However, your question is not about that, but as to why JWs say religious leaders back in the day misunderstood Jesus as claiming to be God. Even if that is taken to include the idea that Jesus was “a god”, which would also warrant stoning to death in the view of those religious leaders, why do the JWs claim that they had misunderstood Jesus? That book states:

“The Jews, however, overlook the fact that Jesus acknowledges receiving authority from his Father. That Jesus claims to be less than God, he next shows by asking, ‘Is it not written in your Law [at Psalm 82:6], ‘I said: “you are gods”? If he called ‘gods’ those against whom the word of God came,… do you say to me whom the Father sanctified and dispatched into the world, ‘You blaspheme,’ because I said, I am God’s Son?”

Without going into any argument as to why Jesus’ quoting of that Psalm need not mean what the JWs think it means, the outstanding question is, why did his explanation not pacify the Jews so that they realised Jesus was not claiming to be God? According to the NWT rendition of Jesus’ next comment, those who ‘misunderstood’ him would have had it completely cleared up when he added, according to their NWT,

“…believe the works, in order that you may come to know and may continue knowing that the Father is in [union with] me and I am in [union with] the Father” (John 10:38).

That could not be clearer, could it? Jesus was apparently denying being God but only claiming to be in union with God the Father. Why, those religious leaders would likely make the same claim of themselves! They were appointed god-like status as representing God on earth, entitling them to respect (not stoning to death), and they were zealously seeking to act in union with God.

This shows that the NWT has Jesus effectively denying being God. The NWT does not give reasons for that slant, but masses of JW literature reiterates their belief that Jesus had a starting point in time, being the first and only direct creation of Jehovah as the Word. This is the basis for their renditions of John 1:1 and 10:33, 38, and why they won’t have Jesus taking the Divine Name, the I Am, to himself.

The problem of how those religious leaders could have possibly continued to ‘misunderstand’ Jesus’ claims here simply increases with the NWT rendition of events. According to the NWT, Jesus is really denying being God. He is making clear that he is merely ‘a god’ and only ‘in union with’ God – not “in God” as all other translations of the Bible state. By changing “God” to “a god”, and “in him” to “in union with him”, that is the same as Jesus saying, “I’m not God! Why are you trying to kill me? I’m not God!”

Of course, we all know that the Bible nowhere has Jesus saying, “I am not God,” but the NWT in those verses comes as close as it can to that. Not because the JWs have misunderstood the words of Jesus, any more than those religious leaders back then did, but because they cannot have their rendition of the Bible saying in any sense that Jesus is God, and that he is in the Father, as the Father is in him. Thus, the NWT tries to have Jesus portrayed as “a god” and saying he is merely “in union with the Father.”

If that is correct, then in the NWT Jesus disabused those religious leaders of a false notion, that he was claiming to be God. He would have taken all the wind out of their sails, and none of them would have picked up a stone to kill him. It is only according to other translations that we see they did not misunderstand Jesus. They knew full well that Jesus was claiming to be God.