if you delete them from your HD using Apple Mail they should be gone from your computer, but if you use a Time Machine backup it would still be on the backup. It is advised you don't start deleting from the backup in this case, it can cause serious problems.
If in doubt and you plan to sell or donate the comptuer, reformat the drive and install a clean copy of the OS which will delete anything and everything permanently from the drive, and follow the directions here.
What to do before you sell or give away your Mac - Apple Support