Why were Red Army Officers and soldiers not prosecuted for War Crimes in WWII?

There is a one word answer to your question: WINNING!

Historically, since the beginning of time, war crimes are for the losers.

And that will never really change.

Some (not all) of Beevor's claims contradict common sense while not showing much in terms of supporting documentation. If you can read Russian, perhaps you should review the following article by N.Mendkovich http://actualhistory.ru/51

I mean, two million raped women in East Germany (Soviet zone of occupation)? Every sixth woman there (including infants and ancient crones) was raped? Anyways, the point is that Beevor bases too much of his writing on anecdotal evdience of the sort "everybody knows that" etc. Of course, everybody knows. Cold war propaganda made sure that everybody in the West knew that USSR was empire of evil that killed and raped evrything in sight. It's kind of tough to try and find reasonable factual basis for all of that now, but who cares? Evrybody knows that's what happened.

1) The Soviet Union had a functional system for trying their own troops. Euromaidan claims the official statistics support 2.5 million Soviet citizens tried (http://euromaidanpress.com/2018/05/15/soviets-executed-three-times-as-many-red-army-soldiers-as-nazis-executed-german-ones/). Not all of these crimes were against the Soviet Union, though many were.

2) Many war crimes were dealt with summarily, such as the reimposition of order on Soviet troops in Berlin after the traditional three days.

3) As part of the constitutive authority for Nuremberg and other European trials the Soviet Union restricted the scope of the trials to their enemies.

4) Many Geneva war crimes were not war crimes under the traditional laws of war and reciprocity that held in the East. As such they could have been acted upon as criminality, or have not been pursued at all.

Your question is based on a false premise. I think it is fair to say that the Red Army soldiers were more violent than the western Allies. Absolute statements like "were [...] not tried" are wrong, however.

And I also think that the Nazis were worse than the Red Army -- as mentioned below, the Soviet leadership wanted to create Communist puppet states, while the German leadership wanted to create Lebensraum.

Two factors regarding the commission and prosecution of war crimes. The first factor explains why crimes might be perpetrated:

• Soviet soldiers had witnessed bitter fighting and German atrocities.
• Soviet war propaganda had highlighted German atrocities and the need for 'payback' to motivate Soviet citizens.

That will explain (but not excuse) why Soviet soldiers committed atrocities, and why Soviet authorities might have been reluctant to investigate and punish. There is a proverb that says never give an order if you know it will not be obeyed.

The second factor explains why crimes might be punished:

• Any army needs to maintain discipline to maintain combat efficiency. A soldier who loots and rapes is not available to fight, and might get into the habit of ignoring orders.
• The Soviet government planned on systematic looting in the form of war reparations and also on the inclusion of Soviet-occupied areas in a Communist zone of influence. The new government followed on the footsteps of the Red Army.

Some Red Army officers were punished by their own commanders.

In a village close to Magdeburg

The officer began to talk, then a German man from a nearby town entered and told through a translator that a Russian soldier has raped his daughter. The man pointed to a soldier.

Then, for the first and hopefully last time, I saw how a person is being beaten to death. The high officer has trampled his soldier to death, all by himself.

Lieselotte B. remembers the victory celebration of the Redarmists on May 8th, 1945

Source: Mirjam Gebhardt, Als die Soldaten kamen; Dieter Hildebrandt, Felix Kuballa (Hg.), Mein Kriegsende. Erinnerungen an die Stunde Null, Berlin 2012, S. 221.

In chapter 5 of the same book (Mirjam Gebhardt, Als die Soldaten kamen / When the soldiers came) the author quotes memories of Eva Ebner, a German woman who was raped, reported the crime to Soviet authorities, and had to identify the rapists:

Now [the Soviet officer] asked me: "Who did that?"

I looked at all of them, seven or eight, and thought: "Now you have the opportunity to pay back for all that pain, for fear and humiliation." This was my first thought. But my second thought was: "Eva, get real. These are people as well. These are the Russians, for which you waited."

I looked from one to another, recognized them, also the small, plump one. He was particularly mean. I looked all of them into the eyes and in them I saw only one thing: fear.

Then I told to myself: "It doesn't pay off, that because of you and your suffering, another one human life is wasted."

According to the author, these rapists would have faced death penalty, had Eva Ebner confirmed their identities.

That's why they were afraid.