Yes, sandpaper is quite capable of removing a tattoo, but it's definitely not recommended: To get to deep layers of skin where the ink is, you'd be risking extensive scarring and infection. Using sandpaper on your skin can also result in an incomplete removal of the tattoo, not to mention an awful lot of pain. Recommended ways for getting rid of tattoos are laser treatments using different types of lasers to break up specific colors of tattoos; surgery to remove the tattoo and suture the edges of the skin together; or creams, which cause the tattoo to fade, although it's still there and slightly visible.
A large percentage of people who get a tattoo end up regretting it, either because they've lost interest in whatever game, motorcycle, or romantic interest they once were so enamored with or because the tattoo is interfering with their new lifestyle (for example, if a tattoo is too visible for a customer service job).
Of interest is Project New Start in California, which offers free tattoo removal to young people aged 13 to 25 who were part of a gang or who are at risk of being part of one. Participants have to commit to a series of rules, such as being part of an educational or steady work environment, doing 50 hours of volunteer community work and staying in touch with mentors. The tattoo removal is done with lasers, and similar to the way other laser treatments work, sessions are spread out over a few months or a year for the skin to heal in between treatments. By removing tattoos that no longer reflect who the person is now, the doctors who volunteer their time to operate the laser machinery give their clients a new start in society.