Why does my World of Warcraft sound lag SO much and how can I fix this

There are a few things to try:

Hit escape and go to Options, then Sound. Check to see that the correct sound device has been selected, otherwise change the sound device. Make sure the settings displayed match your sound card options.

You could also try to update your sound card drivers from Device Management in the Control Panel. Sometimes outdated drivers aren't properly functioning.

Disable any addons that are notoriously spammy, such as damage meters, threat meters and database addons like Atlasloot, chat addons and the like. Such addons may cause general lag issues which manifests itself in the sound being "choppy". If this fixes the issue, turn on the addons one by one until the issue reappears - this addon needs to be updated or removed/replaced.

If all else fails, use the Blizzard Repair utility and have it check for damaged sound files.