Like you destroy all big empires:
Destroy them from the inside. Drive up their war exhaustion to max in every single war. Don't occupy provinces were you actually want them to spawn rebels. If you do that, you won't be fighting one big Mameluks anymore, but several small to middle sized enemies which don't share the same truce timers. If you play it smart you can even play a vassal game: Take one Syrian province in your first war and release them as your vassal. In the aftermath (if you really wrecked them with war exhaustion and maybe one disaster) or else after the next war, all those nice Syrian provinces will flock to your vassal's banner through rebels.
Well I did that, the point is that their empire is homogenous, I had removed all the sirian, iraq and levantine cores and made them release Fez. I guess they blobed too much in that game. They capitalized too much in the chaos of the Ottoman collapse.