Vennaro attended New York Mills High School, Monroe Community College, and the University of Mount Olive.
During his final year at Mount Olive in 2018, he posted an ERA of 0.81 over 44+2⁄3 innings, but still went unselected in the 2018 Major League Baseball draft.
[7] He spent the 2021 season playing with the Double–A Biloxi Shuckers where he made 37 relief appearances and went 1-3 with a 7.61 ERA, 50 strikeouts, and 23 walks over 36+2⁄3 innings.
[10] Vennaro spent the entirety of the 2023 season with Double–A Biloxi, registering a 6.05 ERA with 47 strikeouts and 4 saves across 41 relief outings.
[13] On June 8, 2024, Vennaro signed with the High Point Rockers of the Atlantic League of Professional Baseball.