Where are Profile Manager Configuration Profiles Stored on OS X?
The profiles appear to be stored in

/private/var/db/ConfigurationProfiles/Store/ConfigProfiles.binary


I'd not recommend tampering with it, though.

To see what profiles are installed, and then remove one, assuming you can sudo to the user, you could try:

root$ sudo -u chymb profiles -L
chymb[1] attribute: profileIdentifier: com.stackexchange.apple.test
There are 1 user configuration profiles installed for 'chymb'
root$ sudo -u chymb profiles -R -p com.stackexchange.apple.test