I have a compulsory use mechanical license for my remix. Can I use my song in a video for a commercial advertisement?

You need to look at the terms of your mechanical licenses. They probably give you the right to record the published songs and sell them and pay the songwriters a pre-set royalty rate per unit sold. You probably don't have the right to alter the lyrics or remix the songs, unless you've negotiated and paid for that right.

You don't have the right to use the songs, remixed or not, with images and for ads, since that requires a "synch" license to use any song "synched" with any image. Ads often require special licenses, because the songwriters sometimes have restrictions (e.g., no guns, no politics, no feminine hygiene products) for uses that their publishers/song owners aren't allowed to license, and many have approval rights over all uses.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.