Smith made the team this summer as an undrafted free agent out of San Jose State after the Giants didn't carry a fullback last year. He played only 12 snaps the first two weeks and wasn't on the field for any offensive plays in Sunday's loss to the Philadelphia Eagles.
The Giants also placed veteran linebacker J.T. Thomas (groin) on injured reserve. They signed linebacker Deontae Skinner and promoted linebacker/defensive Cap Capi from the practice squad.
Skinner had spent the summer with the Giants. He was released during final cuts.
Thomas, 29, has struggled with injuries since signing a three-year, $10 million deal with the Giants in 2015. He tore his knee in the opener last season and has taken pay cuts each of the past two years. Thomas has played in just 15 games since signing.
The Giants needed to add linebackers with Thomas injured and starters B.J. Goodson (shin) and Jonathan Casillas (ankle/wrist) in doubt for Sunday when the Giants play in Tampa Bay. Goodson missed the past two games and was limited Thursday.
Casillas didn't practice for the second consecutive day. He spent the afternoon working on the side with a trainer.
The Giants said earlier in the week there was still a role on the roster for a fullback. That role will now probably be claimed by some of the tight ends, including Rhett Ellison.
"There are guys on the roster who are able to line up in the backfield and be a lead blocker. [Rhett] is one of the guys," offensive coordinator Mike Sullivan said. "There are some other guys you can mention, names that are on the roster."
The Giants enter Week 4 30th in the NFL in rushing, ahead of only two teams that have played one less game. They were unable to convert a third-and-short and a fourth-and-goal from the half-inch-yard line against the Eagles.
The thinking was that by having a fullback on the roster this season it would help the rushing attack and diversify the offense. The Giants played almost exclusively (over 90 percent) in 11 personnel last season with three wide receivers, a tight end and a running back on the field.
Sullivan insists the release of Smith will not be a return to last year's approach.
"By no means does the fact that right now with this roster move does it dictate that it is going to be an all Zebra/11 personnel, all up-tempo," he said.