From all the usage I've seen, a tramp stamp is specifically a tattoo on the small of the back - the thought is that then others can gaze upon it when engaging in certain activities in certain positions (as a tramp would).

From my experience, it's about as derogatory as 'geek' or 'nerd' - technically I suppose it could be construed as offensive, but it's become so commonly and inoffensively used, at least by people I know, that it doesn't hold any sting for me, to hear or use.....