Two kinds of crises with speciality properties in piece-wise-smooth systems are reported. The crises are induced by the discontinuity of the systems. The mechanism of the first kind of crisis is a collision between a forbiden region and an unstable orbit located in the region of chaotic attractor. On the contrary, the second one is produced by the collision between a chaotic attractor and a hole induced by the discontinuous regions of the system. For the first one, the scaling laws of the average laminar lenths and its distribution are 〈τ〉∝-1.8 and P(τ)=1〈τ〉exp-τ/〈τ〉, respectively. Meanwhile, for the second one, the scaling laws are 〈τ〉∝exp(k-1/2) and P(τ)=1〈τ〉·exp-τ/〈τ〉).