Evolution can "disprove" God, but only certain types of God. Evolution does disprove the God of Biblical and Quranic Literalism, for starters.

If you think God is needed to explain the diversity of life then evolution disproves your God. If you thnk God is needed to explain the moral feelings of humans and other animals, then evolution disproves your God.

Additionally, if you use God as an explanation of the complexity of nature (like the "fine-tuned" physical constants), evolutionary thought shows this to be a fallacy. Complexity ultimately has to come from simplicity. Complexity is not explained by positing an even more complex Creator. If you would say that God is simple then I would say, in rebuttal, that a God that cannot create a universe is simpler then a God who can.