What is the Biblical basis for the idea that creation will applaud the damnation of a sinner?

This is a euphemism! When he said the "Last thing", it is a figure of speech meaning that it will never happen, as in, "I would never do that! That would be the last thing I would ever do!" Washer was not saying that people or God cheer when people go to hell. It is God's will that none should perish but all come to knowledge of the truth. Washer knows this. You just took his quote out of context because he used an American euphemism. Listen to this rest of the sermon and recognize the context in which the statement was made.

OK. .. so it took a few months of studying and school (working on masters in biblical studies).... I admit I was wrong... I think Paul washer is referencing Rev 19:1-3 when Babylon in all her forms (political, spiritual, etc) is judged...

Rev. 19:1–3 ESV After this I heard what seemed to be the loud voice of a great multitude in heaven, crying out, “Hallelujah! Salvation and glory and power belong to our God, for his judgments are true and just; for he has judged the great prostitute who corrupted the earth with her immorality, and has avenged on her the blood of his servants.” Once more they cried out, “Hallelujah! The smoke from her goes up forever and ever.

This multitude in heaven is rejoicing over the destruction of Babylon in all its forms. The time, therefore, must be just before the second coming of Christ. The multitude is the same group as in Revelation 7:9. Though the general reference may be to all people in heaven, the allusion seems to be to the martyred dead of the great tribulation. The word “hallelujah” appears only four times in the New Testament, all in this chapter (vv. 1, 3, 4, 6). It is a transliteration of the Greek term, which in turn is the equivalent of the Hebrew word. As MacArthur points out, “It is a word often associated both with the judgment of the ungodly and the salvation of God’s people.”1 Poellot appropriately calls 19:1–6 “the New Testament Hallelujah Chorus.”2

The saints here speak with a “loud voice” (cf. 7:10), expressing praise to God in three great words: “salvation,” “glory,” and “power.” The uniqueness of God’s possession of these attributes is emphasized by the definite article that occurs in Greek before each word: the salvation, the glory, and the power of God. God is praised for having judged the great prostitute and having avenged the blood of His servants shed by her hand. This includes both the punishment of the guilty and the vindication of the innocent.3 The ascription of praise is followed by a second hallelujah and the statement that the smoke of Babylon will continue to rise forever. This cannot refer to the city itself, but will be fulfilled by a perpetual judgment of the people who engaged in her wicked deeds. Thus is answered the appeal of the martyred saints in 6:10 for God’s righteous judgment on those who shed their blood.

Excerpt from John F. Walvoord commentaries on Revelation

Thank you guys for setting me strait and making me dig into the Word and research! God bless...

Sometimes we may be quick to judge another brother, not knowing exactly what they mean, so I will not argue for or against this quote, but I will show a way that it is not true, and a way that it could be true.

In contrast, if it is implied that God, or the saints, rejoice in the destruction of sinners, that cannot be true.

Do I take any pleasure in the death of the wicked? declares the Sovereign LORD. Rather, am I not pleased when they turn from their ways and live?
Ezekiel 18:23 (NIV)

In support, if it is merely implied that creation is nature and has been put into bondage by the sin of Adam and groans to have sinners and sin to be taken out of it, this is a personification of nature that seems to be supported by the Bible and may be true.

For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the freedom and glory of the children of God. We know that the whole creation has been groaning as in the pains of childbirth right up to the present time.
Romans 8:20-22 (NIV)