Not only is the location different (a cutie mark would be on the upper thigh/hip on a human, a "tramp stamp" would be above the tail on the lower back of a pony), the intent is different, as is the application.
A cutie mark happens, naturally, when a pony has found her special talent. It is also not only accepted, but expected, as something that just happens. It's more like puberty than a tattoo. A tattoo is something you pay to have put on you, that can, but not always, represent some aspect of who you are. It may or may not be publically accepted, depending.
Personally, I've always hated the term "tramp stamp", because of the implication that any female with a lower back tattoo is a whore. I honestly think it's a lovely place to put a tattoo, but feel I can't get one there because of the public perception of it. I HIGHLY doubt that any little girl watching MLP is going to go "welp, better go get a low back tattoo and start being a slut." It's much more likely that they will see, and identify with, others struggling with wanting to grow up faster, which is a common feeling.