New Orleans had signed West to a one-year deal in June after he spent parts of the previous three seasons with the Baltimore Ravens.
West rushed for 36 yards on seven preseason carries with the Saints over two games, including a 21-yard scamper last week against the Arizona Cardinals.
The 27-year-old veteran was in a battle with Shane Vereen, Jonathan Williams and sixth-round rookie Boston Scott to earn a spot on New Orleans' roster behind Alvin Kamara and Mark Ingram.
Opportunity was present for West since Ingram will miss the first four games of the regular season due to suspension.
By virtue of West's release, at least two of Vereen, Williams and Scott are now likely to be part of the roster entering Week 1.
In 2016, West started 13 games for the Ravens and set career highs with 774 yards and five touchdowns on the ground and 34 receptions for 236 yards and one score.
His production dropped off significantly last season, as he appeared in just five games and finished with 138 rushing yards and two touchdowns.
With a few weeks remaining until the start of the regular season, getting released now could give West a realistic chance to catch on with another team and make the 53-man roster elsewhere.