Out of all the products that are out there for climbing, Dyneema is considered to be the most abrasion resistant. That means that it is the least likely to be cut on a sharp edge, in fact Dyneema is used to make cut-resistant gloves, but that does not mean it's impossible to cut.
Whether or not your sling would be cut by a rock edge depends on how sharp the edge is, and quite frankly if you're dragging you protective gear over a razor sharp edge then you're probably doing something wrong. Features in the rock that could cause damage to your gear or rope must be taken into consideration when lead climbing, if you find yourself in a situation where you are going to be dragging your rope or laying a peice of pro over a ginsu arête, then you should probably consider setting up a new anchor or belay and try to climb around the feature, or setup a short belay with minimal fall potential just to get over it. It may take some extra time, but if the alternative is a potentially tragic accident that leads to a fatal fall, then it's time well spent.
There are products that are designed to protect your rope over sharp edges. if you're climbing a route that you know has a notorious sharp edge, you should probably consider bringing something along in your rack:
Rope edge protector: