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 at some point, but he doesn't dwell on the past. If you have visited Vault 21 and talk to Mitchell again, he will 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, causing Mitchell to settle down there so he could always remain close to her.
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 player a set of weapons (depending on your tagged skills), a Vault 21 jumpsuit (either his own or his late wife's, depending on your gender), and his old Pip-Boy 3000. If the player has one of the pre-order packs, or Courier's Stash installed, the items will be added when the game begins, though can't be accessed until Mitchell gives the player the Pip-Boy 3000.
Prior to leaving the house for the first time, the player can also gain an additional 8 stimpaks if the players 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.
He will only comment on one of your attributes, and only the one at the largest extreme. For example if your highest attribute is Strength at 8 and your lowest is Charisma at 1, he will comment on your lack of Charisma. If you have several attributes at one extreme, he will still only comment on one of them. For example, with Strength and Intelligence at 10, he will comment on Intelligence.