To delete your Mighty Network, go to Network Settings > General Settings. At the bottom of the page, you will see a line that asks if you want to delete your Mighty Network and a link that says "Delete it here."
If you have payments turned on and set up in your Mighty Network, you will need to deactivate any currently active, visible plans first. You can find the option to do this under Network Settings > Get Paid. This will typically take a couple of hours, afterwards you'll be free to delete your network with the instructions above.