During Putnam's true freshman season in 2019, he played in 11 games, finishing the season with 192 snaps.[6] During the 2020 season, he played in and started all 12 games, finishing the season with 790 snaps and a tackle leading the ACC as the only ream to allow fewer than two sacks per game.[7] During the 2021 season, he played in and started 10 games, finishing the season with 633 offensive snaps and was a third-team all-conference pick by Phil Steele.[8] During the 2022 season, he played in and started all 14 games as a first-year center. He finished the season with 996 offensive snaps which was the fourth-most in a season at center in Clemson history. He was also a third-team All-ACC selection.[9] During the 2023 season, he played in and started all 13 games as a permanent team captain, finishing the season with 953 offensive snaps and as a third-team All-ACC selection.[10]
Putnam signed with the Las Vegas Raiders as an undrafted free agent on April 27, 2024.[12] He was waived on August 27, and re-signed to the practice squad.[13][14] He signed a reserve/future contract on January 6, 2025.[15]