Taylor, who signed as a free agent with the Giants this offseason, was among the team's cuts Saturday, as it moved to get down to the 53-man roster limit by 4 p.m. ET.
The Giants are deep at defensive end, with Jason Pierre-Paul, Olivier Vernon, Romeo Okwara and 2017 fifth-round pick Avery Moss on the depth chart. Veteran Kerry Wynn also solidified his roster spot with a strong summer.
Taylor, 27, started 16 games for the Detroit Lions last season, starting opposite Ezekiel Ansah. He had 28 tackles and 4.5 sacks in his first year as a starter. He served as a reserve defensive end for most of his four years with the Lions.
The 6-foot-7, 275-pound South Carolina product, who was the Lions' fourth-round pick in the 2013 draft, has good athleticism and has shown some promise against both the run and pass during his career.
Taylor had signed a one-year, $855,000 contract, but only $40,000 was guaranteed.
ESPN's Michael Rothstein contributed to this report.