You can only delete a mission that you created yourself. i.e. A solo mission or a group mission that you created.
Just log in and go to the mission page
Then from the "Mission Control" menu at the top of the page, select "Delete" mission and confirm.
Note that mission deletion is permanent.
Note that if you delete a group mission, it will be deleted for everyone who is on that mission. Be sure of what you are doing!
If you are on a group mission that was set up by someone else and you wish to be removed from the mission, you will need to make a request directly to the mission admin person for that mission.