Mitchell was born in Vault 21, where he was known by the nickname "Mole Butt" by the younger residents. He left at some point after it was opened, becoming a traveling doctor to help the people of the wasteland. As Mitchell got older, he returned to New Vegas and married his childhood sweetheart. Some time afterward, he retired to Goodsprings, serving as the town doctor.
His wife died after a while, but he does not dwell on the past. Visiting Vault 21 and talking to Mitchell again has him explain that he was going to California with his wife. Due to the weak immune system she had from living in a vault her whole life, she passed away in Goodsprings, forcing Mitchell to settle down there so he could always remain close to her.
When the Courier was ambushed and shot in the head by Benny, Victor brought them to Mitchell for treatment. On October 19, they made a miraculous recovery thanks to the medical care provided by the doctor.
Ain't That a Kick in the Head: Doc Mitchell is ultimately responsible for saving the Courier's life after Benny leaves them for dead. Awakening from the coma, Doc Mitchell runs numerous procedures and tests to make sure the Courier is 'alright.' This serves as a milieu for character building, as well.
Mitchell revives the player after being found by Victor, and sets the characters stats for the game with help of the Vit-o-matic Vigor Tester. He then gives the Courier a set of weapons (depending on tagged skills), a Vault 21 jumpsuit (either his own or his late wife's, depending on gender), and his old Pip-Boy 3000. Having either of the pre-order packs, or the Courier's Stash installed, the items will be added when the game begins, though cannot be accessed until receiving the Pip-Boy 3000.
Prior to leaving the house for the first time, the Courier can also gain an additional 8 stimpaks if the Medicine skill is initially lower than 30 by passing a Speech check (30). An additional Medicine check (30) can be completed after using the Today's Physician on one of his tables, followed by another Speech check (30), again this must be done before leaving the house the first time. All three skill checks reward 30 XP for a total of 90 XP. Similarly, with attribute builds that start both Speech and Medicine above 30 (e.g. Int 10, Chr 10, Luck 7), Medicine can be temporarily lowered by drinking alcohol (e.g. from Mitchell's refrigerator) to temporarily lower it below 30 and enable passing all three checks.
He will only comment on one attribute, and only the one at the largest extreme. For example if the highest attribute is Strength at 8 and the lowest is Charisma at 1, he will comment on lacking Charisma. With several attributes at extreme, he will still only comment on one of them. For example, with Strength and Intelligence at 10, he will comment on the latter.