It's not sensible or safe to do so, and you'd experience serious pain. The power needed depends on the focus and colour, since red is hardly absorbed by skin. Violet would be best if you're stupid enough to try, and the more power, the quicker it is. Focused, 75mW would be enough to singe skin. Doing so would be beyond stupid though.
Laser branding
The technical term for laser branding is "electrocautery branding". The electrocautery unit is more like an arc welder for skin than a medical laser (though it is possible to use a medical laser for scarification) Scarification - Wikipedia, the free encyclopedia