Laser cutters, plasma cutters, and cutting torches all use the same method to cut - a point is heated until it's hot enough to burn, then oxygen is blown into it.

The difference is the heat source and how small of an area you can heat up.

I haven't tried to cut anything in a vacuum, but i think it would work with adjustments. The oxygen or nitrogen is bottled for the laser anyway. (Or rather its stored as a liquid in tanks outside)

A laser doesn't cut any more than a flashlight or a microwave. It just makes things hot.