Update:
Due to the way WoW sound files now work, addons of this type are broken for the foreseeable future. Muting sounds now requires an in-game addon, such as the new MuteSoundFile. Replacing sounds effects with other sounds is not possible at this time.
If you're looking to mute this sound effect with MuteSoundFile, the file ID is 562388.
This simple addon replaces the "TigerStand2" sound effect with a blank sound file. Works whether you're a hunter looking to mute their own pet, or another class who is annoyed by noisy kitties in the auction house.
Note that this does not mute the various "roar" sound effects made by some hunter pets and druids in cat form, only the extended "yawn with added slobber" one.
Rather than being installed in your Interface/Addons folder, this addon should be placed in the "_retail_" folder. It will not appear in your in-game addon list, but will work automatically and should not need updating after patches.