Born in Westerville, Ohio and raised in Galion, Shuck went to Galion High School. At Galion High, he batted .576 with a 1.650 OPS and had a 1.12 ERA with 134 strikeouts in 69 innings, and also lettered in basketball. Shuck went to Ohio State University where in 2006, as a freshman, he batted .325 in 123 AB as a hitter, and led the team in ERA as a pitcher. He was named the Big Ten Conference Freshman of the Year. In 2007, he hit .382 and had a 4.89 ERA. After the 2007 season, he played collegiate summer baseball with the Cotuit Kettleers of the Cape Cod Baseball League. In 2008, he hit .356 and had a 4.29 ERA and led the team in strikeouts. Shuck was drafted in the sixth round, 182nd overall, by the Houston Astros as an outfielder in the 2008 MLB Draft.

Shuck played 2008 with Short-Season Tri-City, where he hit .300 and was a New York–Penn League All-Star. He played with High-A Lancaster in 2009, where he hit .315 with 18 SB and 36 RBI. He started 2010 with Double-A Corpus Christi, where he was a Texas League All-Star, hitting .298 with 28 RBI in 101 games before earning a promotion to Triple-A Round Rock. After the Astros and the Texas Rangers switched affiliates, Shuck started 2011 with Oklahoma City, where he was a Pacific Coast League All-Star, with a .401 OBP in 101 games before earning a promotion.

On August 5, 2011, Shuck was called up to the majors to replace Luis Durango, who was designated for assignment. In his first major league at bat, he hit a single off Milwaukee Brewers’ Yovani Gallardo and stole second.

Shuck signed a minor league contract with the Los Angeles Angels of Anaheim as a free agent in November 2012 with an invitation to spring training.

On July 29, 2013, Shuck hit his first career home run against the Texas Rangers. He appeared in 22 games for the Angels in 2014 and hit .167, but he had spent most of the season with the team’s Class AAA minor league affiliate, where he hit .320.

On November 9, 2013, Shuck married Christine Anne Cimino at the University of Notre Dame, making him the second professional baseball player to marry into the Cimino family: Christine’s sister, Mary Catherine Cimino, is married to pitcher Mark Melancon.

On September 5, 2014, Shuck was traded to the Cleveland Indians for cash considerations.

On November 3, 2014, Shuck was claimed off waivers by Chicago White Sox.

On June 8, 2016, Shuck pitched for the White Sox against the Washington Nationals in the top of the 9th inning in an 11–0 game. He allowed one hit, one run, did not walk or strike out anyone, but he got Bryce Harper to ground out. He was outrighted on November 2, 2016.

On December 17, 2016, Shuck signed a minor league deal with the Twins. He elected free agency on November 6, 2017.

On November 24, 2017, Shuck signed a minor league contract with the Miami Marlins. He had his contract purchased on April 13, 2018. He was designated for assignment on July 5. He hit .192 with 4 RBI’s. He declared free agency on October 2, 2018.

Shuck signed a minor league deal with the Pittsburgh Pirates on January 30, 2019. On March 28, it was announced Shuck had made the Opening Day roster. Shuck was designated for assignment on May 4, 2019 and outrighted on May 8. On May 18, it was announced that Shuck would attempt to become a two-way player, splitting his time between pitcher and outfielder. He elected free agency on October 1.

On February 12, 2020, Shuck signed a minor league deal with the Washington Nationals. He was released on May 30th.