Does an Eved have an obligation to give himself a Mila? According to Tosfos that says it's a Mitzva Asei SheHazman Grama, so the Eved is not obligated, just like a woman. Even according to the Ritva, only if your doing the Mitzva on someone else would we say he might be obligated. But here, the Mitzva is on himself, so it's like all other Mitzvas Asei SheHazman Grama which he's exempt from.
But the Turei Evan has a different approach.