Victor Mancini was born in Hancock, Michigan, where he played minor hockey for the Honeybaked, Compuware and Little Caesars programs.

In 2019-20, Victor left the United States to play in Sweden joining the Frölunda junior 18 elite team and eventually graduating to their under-20 team where he was named captain.

Upon his return to the United States in 2021, Victor joined the Green Bay Gamblers of the USHL playing in 33 games before committing to play at the University of Nebraska-Omaha the following season. In 2021-22, Victor played in 38 games for Nebraska-Omaha as freshman.

Despite being passed over in his two first NHL draft eligible seasons, the New York Rangers selected Victor in the 5th round of the 2022 NHL Entry Draft. Victor returned to Nebraska-Omaha in 2022-23 suiting up for 38 games while notching 8 points. Off the ice, Victor was recognized for his efforts in the classroom being named NCHC Academic All-Conference and a Distinguished Scholar. In his third NCAA season in 2023-24, Victor set new personal bests for games played and points.

Following his junior season, the New York Rangers signed Victor to a three-year entry level deal. Victor made his pro debut the following day for the Hartford Wolf Pack of the AHL. He would go on to play 7 regular season games and 10 playoff games for Hartford. On October 9, 2024, Victor made his NHL debut for the New York Rangers playing 17:27 in a 6-0 win over the Pittsburgh Penguins.