The only thing you can figure out is average power as a rating in mJ means the laser is pulsed. To do this you also need to know the repetition rate. By the way 1.5J is quite a bit of energy for a small laser.
Tatoos are mostly black and green ink. -Primary absorbers of red and infrared energy. Human skin does not absorb IR that well, so it's the tattoos that receive the real damage; carbonizing the inert pigments, so they can be processed out by the body.
Same process that lets you pop a red balloon inside a clear balloon with a green laser.