Police said the victim, a 34-year-old old man, was stabbed in the back and the wrist. His injuries were described as life-threatening and he remains at John Radcliffe Hospital, Oxford.
READ MORE: Faringdon Road shut by police
Four men, all from Swindon and aged 17, 22, 24 and 30, have been arrested on suspicion of causing grievous bodily harm with intent. They remain at Gablecross police station.
Detectives have asked for anyone with dashcam footage of Faringdon Road and Cambria Place at the time of the stabbing – around 6am on Boxing Day – to contact police via the 101 non-emergency number.
Information can be reported anonymously, via Crimestoppers, on 0800 555 111.