The next year, Cervenka played for the Low-A Lowell Spinners, posting a 2–4 record and 3.59 ERA with 55 strikeouts in 62.2 innings pitched.

In 2011, he split the season between Lowell and the Single-A Greenville Drive, struggling to a cumulative 2–10 record and 7.93 ERA in 22 games between the two teams.

[3] He spent the remainder of the season split between the Single-A Peoria Chiefs and the High-A Daytona Cubs, accumulating 47 strikeouts in as many innings.

He split the 2013 season between Daytona and the Double-A Tennessee Smokies, logging a cumulative 6–1 record and 3.00 ERA in 41 appearances between the two teams.

He was invited to major league Spring Training in 2015, but did not make the club and was assigned to Tennessee, later receiving a promotion to the Triple-A Iowa Cubs after 3 stellar games in Double-A.

[9] He made his MLB debut the next day, allowing a single to Washington Nationals infielder Daniel Murphy, the only batter he faced.

On August 6, 2016, the Braves traded Cervenka to the Miami Marlins in exchange for Anfernee Seymour and Michael Mader.

[10] In 18 games for Miami in 2016, he logged a 4.82 ERA with 7 strikeouts in 11 innings of work, also spending brief time with the Triple-A New Orleans Zephyrs and the Double-A Jacksonville Suns.

[15] He split the remainder of the season between the High-A Lakeland Flying Tigers, the Double-A Erie SeaWolves, and the Triple-A Toledo Mud Hens, accumulating a 3–2 record and 1.77 ERA in 29 games between the three teams.

On April 15, 2021, Cervenka was traded to the West Virginia Power of the Atlantic League of Professional Baseball in exchange for a player to be named later.

On June 17, 2021, Cervenka was traded to the Long Island Ducks of the Atlantic League of Professional Baseball in exchange for a player to be named later.