You can choose to leave a Mighty Network you belong to by going to your Profile Image > Personal Settings > Account > Leave this Network.
From here, if you choose to Leave this Network you will instantly leave the network and you'll stop receiving notifications. However, keep in mind that when you leave a network, your activity (such as any comments or posts that you added) will still be visible to other members.
How to Leave a Group
If you only want to leave a Group that you belong to within a Mighty Network, first you need to make sure you're signed in on the web.
Then, just go to your Profile Photo > Your Settings > Account. You will see a list of Groups you below to, and you can leave the Group by clicking on the Leave button next to that group.