Stepney started in Formula One as a mechanic at Shadow in 1977. He followed Elio de Angelis to Lotus before moving to Benetton for the late 1980s and early 1990s, later joining Scuderia Ferrari to work with Michael Schumacher, Rory Byrne, and Ross Brawn. At Ferrari, he served as chief mechanic and later became race and test technical manager.
At the 2000 Spanish Grand Prix, Stepney was injured during a pit stop for Schumacher's car when the driver was signalled to depart while Stepney was still detaching the fuel rig. He suffered badly damaged ligaments to his ankle.
On 1 February 2007, it was reported that Stepney was unhappy with Ferrari's technical restructuring and that he wanted to leave the team, seeking a new challenge. While Ferrari initially stated he would remain under his contract, Stepney was promoted to head of performance development on 23 February 2007, a role that meant he would no longer have to attend races.
On 21 June 2007, reports emerged that Stepney was the subject of a criminal inquiry by the Modena district attorney following a formal complaint by Ferrari. A Ferrari spokesman told Reuters the investigation was "not related to any event; it is related to his behaviour." Stepney was also accused of selling Ferrari parts to competing teams. He denied the accusations and claimed to be the victim of a "dirty tricks campaign."
Stepney was dismissed by Ferrari on 3 July 2007. The same day, Ferrari announced legal action against Stepney and McLaren engineer Mike Coughlan concerning the theft of technical information. Following his return from holiday on 5 July, Stepney was interrogated by Italian police. On 6 July, Honda released a statement confirming that Stepney and Coughlan had approached the team regarding "job opportunities" in June 2007.
On 22 January 2008, Stepney was recruited as Director of Race Technologies by Gigawave, a manufacturer of on-board racing car camera systems fielding a team in the 2008 FIA GT Championship.
On 7 March 2008, the FIA issued a statement urging teams and licensees not to hire Stepney without "conducting appropriate due diligence regarding his suitability for involvement in international motor sport." The FIA noted that Stepney had admitted to passing confidential Ferrari information to an employee of Vodafone McLaren Mercedes and had apologised, though he disputed the "seriousness and extent of his involvement."
This recommendation remained in place until 6 February 2009, when the restriction was lifted. FIA president Max Mosley claimed at the time that Stepney and Coughlan had only been "minor players" in the scandal. On 27 August 2010, Stepney was appointed team manager of the Sumo Power team in the FIA GT1 World Championship. He also served as team manager and chief mechanic of JRM Racing in the FIA World Endurance Championship.
On 29 September 2010, Stepney was found guilty of "sabotage, industrial espionage, sporting fraud and attempted serious injury." He was sentenced to 1 year and 8 months in prison and handed a €600 fine. The sentence was reportedly reduced after he entered a plea bargain, and Stepney did not serve any time in prison.
Stepney was killed on 2 May 2014 in a road traffic incident on the M20 motorway at Ashford, Kent. According to police, his vehicle was parked and he appeared "to have [entered] the carriageway and was then [subsequently] in collision with an articulated goods vehicle." He was pronounced deceased at the scene. A subsequent Coroner's inquest "concluded it was a suicide," but also stated they "found no reason for Mr Stepney to take his own life" and recorded an open conclusion.