Dwoskin was born in Brooklyn. He contracted polio at the age of nine and underwent a grueling rehabilitation that entailed confinement in an iron lung, muscle transplants and relearning to walk, painfully, with crutches. He spent four years in the hospital before he was discharged. Dwoskin used crutches for much of his life. Poliomyelitis progressively restricted his mobility and in later life he used a wheelchair.He studied at Parsons The New School for Design as a student of Willem de Kooning and Josef Albers, and at New York University. After working as a graphic designer and art director for CBS and Epic Records, he made two short films, 'Asleep' and 'American Dream', in 1961 and became part of the bohemian world of New York 'underground' filmmakers. He received a Fulbright Scholarship to move to London in 1964, where he remained until his death.
Dwoskin became a key figure in British avant-garde cinema. He was a co-founder of the London Film-Makers' Co-op.
He wrote two books: Film Is... in 1975 about the International Free cinema (published by Peter Owen, UK and Overlook Press, US) and Ha Ha! in 1993 (published by The Smith, New York, 1993).
In 1967–1968 he won the Solvey Prize at the Knokke Experimental Film Festival in Belgium for a series of short films which established his reputation. His films have been screened worldwide including festivals at Cannes, Berlin, Rotterdam, Toronto, Lucarno, Pesaro, Mannheim, Oberhausen, Sydney, Melbourne, Hamburg, San Francisco, Turin, Riga, Madrid, Barcelona, andBenalmádena amongst other places. In 2009, the BFI Southbank in London presented a season of his work.
Dwoskin also made documentaries: ‘’Pain Is...’’ and ‘’Face of Our Fear’’. ‘’Face of our Fear’’, a film that addresses attitudes about disability, was commissioned by Channel Four, UK, and broadcast in 1992.
Awards include L'Âge d'or prize, Brussels Film Festival 1982, the prestigious DAAD Fellowship (Berlin) in 1974, and the Rockefeller Media Fellowship in 1994.
He was a respected teacher and lecturer, holding positions at London College of Printing and Royal College of Art, London; San Francisco Art Institute and San Francisco State University, USA;University of Geneva and l'École Supérieure d'Art Visuel, Switzerland.Retrospectives of his work were held in New York, London, Madrid, Barcelona, Paris, Brussels, San Francisco, Geneva, Lucerne, Digne, Berlin, Marseille (1995), Bilbao (1996), Strasbourg (2002), Paris/Pantin (2004), Rotterdam (2006), Lucca,(2006), Bruxelles (2006), Lussas (2008), London (2009), and Berlin (2009).