You can uninstall any applications you don't want, but I would be careful about graphics drivers/network drivers, X-server and desktop themes, as well as the GUI login manager (x-server client, such as mdm, gdm )
--you can find the installed programs under synaptic ( a gui package manager)
You may not want more than one graphics applications, or may only want a vector based(scales well for drawings/images..) or a bit-mapped one, such as a paint program (better for photographs))
The number of applications installed won't really slow down the system, if they are not being loaded (they simply take up some storage (hard drive) space
--however you can eliminate quite a few processes that are loaded, and possibly some modules, depending on your system configuration -- this does in fact slow down the system, by taking up some RAM that you could use more effectively for your preferred/running applications
- You do need to research for the names of these process: services in ubuntu/mint terminology (there is a Gnome GUI screen that can show you the running services/processes)
--check their names under Ubuntu to see what their purpose is: for example unless you need or want detect devices (printers/networks) as they are connected, you don't need the avahi service
Being careful in what you want to attempt removing from the system is the watchword..http://www.addictivetips.com/ubuntu-lin ... ntu-linux/