Hi Bradley,
Yes this is entirely possible but just a heads up, this can get frustrating for viewers. To mute discord audio from your stream, you have to fiddle with your OBS settings.
In OBS, you can choose to only add certain audio sources, but discord can be muted entirely. For example you can add your microphone, but you don’t need to add the desktop audio, which is the source where your friends are chatting.
Navigate to the “Audio Mixer” panel located at the bottom of the interface to proceed.
Select the Discord audio in the “Audio Mixer” panel and adjust the volume using the slider.
To completely mute the audio, simply move the slider all the way to the left in the Audio Mixer panel.
Hope this helps.