The NFL gave the Giants and Jets a couple of extra days to reach the limit because Hurricane Irene delayed their game until Monday night, forcing the teams to play twice in three days.
The Giants must cut another 27 players to reach the 53-man limit by Saturday evening.
Sintim, a third-year pro, tore the anterior cruciate ligament and patellar tendon in his right knee early in the second half against the New England Patriots on Thursday night.
Burks, Clouser and Abdulai are rookies. Watkins is a third-year pro.