Oh man could you pick a worse target; you're not gonna cut a watermelon with a laser, it's big, round and wet. You could probably scorch your way through eventually though.
Lasers don't really cut things like in movies, a laser cutting machine can only manage fairly thin materials. Thick plates of steel or w/e are usually water cut.
It's all down to physics really, your laser is essentially just focussing heat onto a very fine point. Anything that's going to resist or absorb that energy isn't going to be affected much.
Laser weaponry theoretically functions by causing heat stresses; superheating a point on the target to the point where the material expands, explodes or combusts. Blowing up a watermelon with a laser is doable I guess. The US Navy are operating a small laser weapon with a maximum of 30kW; that's a bit more than your average pointer.