Yes, there is a claim that Mountain Dew can dissolve small animals. No, this is not true, depending on how you’d define dissolve. For the purposes of this question, classify dissolve as “(with reference to a solid) become or cause to become incorporated into a liquid so as to form a solution.” In simpler terms, imagine the solid object having to completely dissolve. CBS news says that, according to court documents quoted by legal newsline, “the mouse would have become a ‘jelly-like substance…’” Furthermore, this was backed by CBS quoting; “It's not the first time the soft drink giant has faced an ugly lawsuit: federal regulators in 2009 said a "disgusting" blob found in a can of Diet Pepsi was probably a frog or toad.”
While none of the links work in the modern day, there are a variety of other news sources that dictate the same information, such as ABC news. Granted, in that article, it was definitely written with entertainment value in mind. As for the “frog in a can” incident, that was also written about in various articles, including the Australian Broadcasting Corporation.
I could not find transcripts of the case itself, so there is no primary source, sadly. However, regardless, it does not seem that small animals can be completely dissolved in a can of Mountain Dew. So if you find one in your drink, you’ll at the very least know.
Sources:
https://www.cbsnews.com/losangeles/news/pepsico-no-dead-mouse-found-in-mountain-dew-soda-would-dissolve-carcass/
https://www.abc.net.au/news/2009-09-04/dismembered-frog-found-in-pepsi-can/1416550
https://abcnews.go.com/blogs/headlines/2012/01/mice-no-match-for-mountain-dew
https://www.abc.net.au/news/2009-09-04/dismembered-frog-found-in-pepsi-can/1416550