There's 2 things that kind of screw with the limited power set idea of the swap in the case of Mordecai.
A) He has a ton of knowledge and experience. If the story has learnable power, his growth would be unparalleled. If swapped with a protag in the same setting, the 'does not have his powers' is partially nullified just because being himself in that world means he has access to specific forms of magic immediately, including divine prayers. Removing the requisite knowledge would mean it's not really the same character, as that knowledge is part of a long history and who he is. At a minimum, in a completely mundane world, he would be a martial artist without equal, because no martial artist in a mundane world can have hundreds of years of experience.
B) Even skipping the magical aspects, Mordecai's current avatar is biologically super-human. You can't turn off that particular level of enhancement other than arbitrarily deciding that he's going to have a body of specific statistics. There is no 'normal' level to his body, the 'depowered' version is incredibly sturdy, strong, fast, has extraordinary biological senses, etc. He doesn't even have blind spots in his eyes: the light sensing cells are flipped the sensible direction, so there is no need to have a hole where the nerves pass through. It's basically an Nth iteration of genetic engineering.
I am assuming he's crammed into his avatar; a crystal core without any powers of any sort is just an inert hunk of rock, and as a magical life form would probably instantly die.
Running with that idea and dropping him in any cultivator world would see him puzzling out what the hell is going on, then noticing that chi flows differently in this world than in his own (as he knows how to channel chi already, power reset would be because of world differences). Learns the very basics of cultivation to make sure he's on the right path, and then speed runs the cultivation process until he can transcend realities.
I think a LitRPG system would have conniption fits. A new entry/level 0 with his physical stats, skills, and knowledge does not compute! Exact results vary with the system. Dumb systems are going to assign him level 1 and then rapidly give him "defeat X over your level" type feats because it has failed to recognize his actual skills and physical prowess. Smarter systems will be able to adjust and work out his correct level and powerset.
A world with different magical rules than his own is mostly a matter of learning the new rules, so long as magic is learnable. He has skills like visualization, conceptualization, memorization, and mathematics already covered.
Anyway you look at it, his primary goal will be getting back home. He might solve local problems along the way, he has too much empathy not to, but his free time will be about learning enough of the local power system to get back to his home world. Even a supposedly mundane world clearly has *some* magical influence, or the swap couldn't have happened.