University officials said Friday that Clemson would not renew Smith's contract that expired last month.
Clemson basketball coach Brad Brownell said he supports the decision to let his seven-year assistant go.
Smith said in the July 2017 video "if you do it and use resources at Clemson, like you can really keep everything tight."
Later in the video, Smith said, "It's a small college town. You can come to a game one night, after the game, you seed a dude out there in a nice looking suit, you like, 'wait a minute now.'"
Testimony from financial adviser Marty Blazer indicated he believed that meant boosters would give players improper benefits.
Dawkins and amateur basketball coach, Merl Code Jr., are charged with paying bribes to assistant basketball coaches to help secure NBA-bound players as customers. Ex-assistant coaches at Arizona, Auburn, Oklahoma State and Southern Cal have pleaded guilty to bribery conspiracy and await sentencing.
Clemson started a review of its football and men's basketball programs after the wiretap was played in court.
"We feel very strongly that those were unfortunate comments and we are doing our due diligence, but there is no reason to believe, and nothing that we've been able to find at this point in time, that implicates the football program in any of that," Clemson athletic director Dan Radakovich said.
Radakovich met with Brownell and Smith this week.
Clemson football coach Dabo Swinney told The State newspaper of Columbia at a booster club event that Brownell had reached out to apologize for Smith's comments.
Swinney was disappointed with the characterization and is proud of how he runs his program.
"We've always been a program committed to doing things right way and we always will be," Swinney said.
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