That low-pitched buzz is obviously a cat growling at the mouse whenever it moves. If the tape-like tweeting is a canary then it's probably a Sylvester, otherwise a Tom.
More seriously, it sounds like old-fashioned analogue interference. The audio pitch of the interference matches the mouse signalling data rate - movement has higher resolution than scrolling. The mouse circuitry is leaking the signal as electrical noise and the audio analogue output circuit is picking it up. Hard to say whether the mouse circuit is leaking more noise than it should or whether the audio is more sensitive than it should be.
Do your headphones plug directly into the PC or a separate audio system?
Typical causes include: an earthing problem, otherwise known as the 0 V line. Could also be a common +V supply rail. One of the connectors might be loose, dirty or faulty, or even the mouse itself. Do the audio and mouse sockets share a common wiring connection back to the motherboard? Do you have a spare mouse and/or headphone set with connector that you can try?
If all that checks out, there's probably a fault on the motherboard (or in the separate audio box, if present) - a failed decoupling capacitor, a dodgy soldered joint, a failing chip, something like that.
"Klinger, do you know how many zoots were killed to make that one suit?" — BJ Hunnicutt, 4077 M*A*S*H