Yes. Each type of tattoo pigment can be removed with different types of light wavelengths. Since black pigment absorbs all laser wavelengths, its actually the easiest to removewhich is fortunate considering its the most difficult color to cover up with makeup or another tattoo.
Darker pigments like brown, red, green, and blue can typically be removed without extra sessions. However, lighter pigments like yellow, pink, and orange are usually the most difficult to remove. In the past few years, tattoos using white pigment have become a trend but experienced tattoo artists will suggest you avoid choosing this color in the first place, as its nearly impossible to remove.