There is no direct connection from Putney to Stratford. However, you can take the train to Waterloo Underground Station then take the Tube to Stratford Underground Station. Alternatively, London Underground (Tube) operates a vehicle from Putney to Stratford every 10 minutes. Tickets cost $4 - $7 and the journey takes 53 min.
From Putney train to Waterloo Underground Station then Tube to Stratford Underground Station. 40 min £8. From East Putney Underground Station Tube to West Ham Underground Station. 53 min £4. From Putney taxi to Stratford. 28 min £54. From Putney drive to Stratford. 28 min £2. From Putney Uber to Stratford. 28 min £28. From Montserrat Road , Putney Bikeshare to Stratford Station, Stratford. 1 h 26 min.