Using Mambo version 4.6.4, and the readme for the install says:

"NOTE: Mambo 4.6.0 - 4.6.4 don't handle multiple xml files properly, so you need to first unzip comprofiler.zip, remove the file and re-zip before installing on these Mambo versions."

There are three xml files in the com_comprofile root:
- comprofile, comprofilej, metadata
plus database.cbcore (in the database subfolder) and cb.lists (in the xmlcb subfolder).

Which one(s) do I take out? And once it is removed what do I do with it (the removed file)?

I 'think' (as I dont use Mambo) the only ones you need to worry bout is the comprofile.xml and comprofilej.xml, From what it sounds like the instructions are saying is your extracting the .zip file and then go into the newly created folder you made with the extracted archive and remove one of those xml files since they both have install instructions. (I would venture to guess comprofilej.xml but dont hold me to it) Once that file is removed zip those files back up into a new com_comprofiler.zip archive. Then install with this new com_comprofiler.zip

*Make sure to make backups*