To remove a tattoo, the laser we use is called a 'Q Switch' laser, or an ultra short pulse laser. They are extremely hot, fast and operate in a very narrow frequency.
To break these prticles, the laser heats up which, due to thermal expansion will cause the paticle to expand, but the zap has to be quick enough so that half of the particle remains cool. These 2 different temperatures then rip the ink particle apart.
This process is called photothermolysis.
Once these particles have ben broken down, the white blood cells carry on engulfing as tehy normally would, but now these particles are much smaller.