Quantum mechanics doesn't work well with general relativity (gravity), but it works just fine with special relativity. Special relativity still has a concept of spacetime, it's just that the spacetime is flat, not curved like in general relativity.

(In fact, you can even do quantum mechanics in curved spacetime, as long as the spacetime has a predefined fixed curvature. But in GR, the curvature depends on how the matter and energy inhabiting the spacetime are distributed. That is what gives quantum gravity theorists trouble.)