Is there a way to delete something off your computer but not your itunes account?
There are several ways. 

Easiest, but most costly is to subscribe to iTunes Match service which will let you download your entire library on another device and keep it in the cloud for you.  

Harder, but relatively cheaper is to migrate your iTunes library to another computer. 

Migrating iTunes library when replacing the hard disk

Middle-ground is to enable home sharing which is a simple way to transfer. 

transferring itunes

Then afterwards delete songs from old comp. easiest thing to do for that is delete it from iTunes and agree to also remove the file and remove from library (on this computer). Old files will be in the trash bin until you empty it.