A 1000 W laser is roughly one million times more powerful than a typical small laser pointer. A laser metal cutter often uses a laser of roughly this strength; more powerful versions pack up to 10000 W. An industrial laser demolition gun (yes, this is extremely cool-here’s a video) brings roughly 5000W of power. These devices sure look tough enough to put some damage on some skin.
Considering all of the above, it seems that we need no less than 1000 W and ideally more like 10000 W of power for our blaster.

Current cutting edge handheld laser weapons are puny by comparison with those numbers. A 1990’s model had about .015 W. That’s not even enough to cause a skin burn. The power of the laser in these new Chinese weapons is unclear, but it’s likely no more than 10 W: Short on power by a factor of 100 to 1000. A laser of this strength can light a match or burn a small hole in a sheet of paper, but no way they can blast a hole in a person. Working in laser labs I can say that while a brief exposure to a laser of this power will leave you with a small burn, it’s nothing medically serious.

All of the above ideas consider that the laser hits someone directly on bare skin. Of course that’s not too realistic.