The annoying this is that most of the time, your computer speakers / headphones / laptop audio are much better then the monitor or TV ones.
The reason why the audio cut off is that DisplayPort connections have an audio stream, which means that when you connect it to a monitor or TV, it will detect it and switch the audio to that device automatically. So you just connected a DisplayPort enabled monitor and your computer or laptop sound just cut off? Well, here's how to fix all your DisplayPort sound problems.
DisplayPort Fixing Sound 'Not Working' Problem