You don't need the notion of mass here, it's purely kinematics. From the Lorenz transformation you see that if something traveled from A to B faster than light, then there is a reference frame in which the arrival to B happened earlier than the departure from A. If you want to do the math yourself, which is actually quite illuminating and only requires high school math, then consider a reference frame moving very fast (but slower than light) in the direction from A to B. So, traveling faster than light would lead to the problems with causality similar to time travel.