There is no hard delete option for PROFILES. But you are archive the profile if you do not need to the profile. Archiving a profile will remove the keyword profile from the list and put them in the ARCHIVE of the account.
Archived profile stores the data till 3 months maximum after which the data is deleted from the system. Within those 3 months, if you want to un-archive the profile you can do it. The data will be restored for only the keywords, which had been tracked.