its not that antimatter has negative mass but if it were to come in contact with a 'normal' particle it would cancel it out.
i.e. a positron + electron = nothing
In positron electron annhilation you wouldn't get nothing. Depending on the energy (how fast they were moving), you could get a few photons (if low energy) or you could create a higher mass particle anti-particle pair (if high energy) with the extra energy leading to the rest mass of the particles. You could even create force particles for the weak force (we call them Z, W- and W+) from an electron positron pair.