Disabling all sounds and beeps on Linux

"I'm assuming that you mean the PC Speaker beep, because the beep in a connected speaker would be easy to remove by just turning off the speakers.

See this answer on server fault, but the jist of it is:

modprobe -r pcspkr

on the command line, and add

blacklist pcspkr

to the /etc/modprobe.d/blacklist.conf file.

Newer kernels use the snd_pcsp module instead, so if it doesn't work, try the same two things as above except with snd_pcsp in the place of pcspkr"

Not exactly Linux-specific, but I've been known to unplug the speaker wires from the motherboard. Unfortunately, not all computers like to be opened up while running.