"Is there a way to wipe its memory and use Linux on there, too?"
The version of Linux that runs on small devices such as hand held computers and mobile phones is called embedded Linux. I use it on a Sharp Zaurus handheld.
You could check with Google to see if anybody has ported embedded Linux to the Handspring Visor.
If nobody has done so already then porting embedded Linux to a new device yourself is a major project. You can get some can get some information at:
http://linuxant.hit.bg/Embedded-Linux-Howto.html
Also Red Hat support has some information about embedded Linux.