Is there a way to silence/stop particular sound effects, especially on the main screen? [closed]

Open the console (must be enabled in Keyboard Advanced Options- default key: '~').

Enter this:

sv_cheats 1
stopsound

(You can bind this to a key with something like bind KP_ADD "sv_cheats 1; stopsound".)

Alternately, you can override the Saxxy sound resources with silent ones.