He can be tank, he can be a DPS, but most people opt for TANKY DPS.
Anyways settle a debate with a friend, he says Mundo's primary role is to tank.
I think tanks should have:
1. A initiator skills (powerball, shen's dash)
2. A disable, slow doesn't count (taunts, stuns .etc)
3. High base hp/defense
4. A damage reduction skills (defense ball curl, shen's ult .etc)
Mundo has cleaver, but a slow doesn't disable, no imitator skills unless you count his ultimate...which is basically just ghost.
Then there are offtanks that potentially can be a tank, but usually shouldn't like Nunu, Nasus .etc