'do a mission' is correct and can be used in written English.
Example sentence: Our team is determined to do a mission to save the endangered animal species.
"But I'm here to do a mission".
"The world is moving to new uses of space, and our technology in the United States has not progressed because of the time and expense it takes us to do a mission," said Robert Conger, vice president of Microcosm Inc., a small company that is working to perfect a low-cost launching vehicle at its factory in Hawthorne, Calif.
Uganda had always been her dream place to do a mission trip.
Never do a mission without a plan.
Make everything you do a mission.
In these games, there is usually more then one character to do a mission from the viewpoint of.
"He showed me where he jumped out of an airplane in the dark, swam seven miles, did a mission, and then swam seven miles back," Ibanez said.
Like that time you and your friends were doing a mission together and this happened and then that happened and it was so awesome and then supposedly you're still talking about it years later.
