There is no way to mute "Role Pings" on Discord currently. You can mute @here/@everyone/@your name, but if you are assigned a role and that is pinged, it goes through.

That is one of my main gripes with Discord, in addition to:

1. Uploading photos/videos through the mobile app stops if you lock your phone or background the app. No other modern app exhibits this behavior.

2. Blocking users shows a large "BLOCKED" message, with no option to truly block them.