Morris was drafted by the New York Mets in the 10th round of the 2010 Major League Baseball draft.[3] He made his professional debut that season for the Gulf Coast League Mets. He appeared in eight games with six starts, going 1–1 with a 2.19 ERA and 28 strikeouts over 24+2⁄3 innings.
Morris played 2011 and 2012 with the Kingsport Mets.[4] He played 2013 with the Brooklyn Cyclones, and was 4–1 with one save and a 1.00 ERA in 45.0 innings, and was fifth in the league with 12.0 strikeouts per 9 innings, and 10th with 5.8 hits per 9 innings.[5][6]
After splitting time between starting and relieving his first four seasons, Morris became a full-time reliever for the Savannah Sand Gnats of the South Atlantic League in 2014. In a game against the Augusta GreenJackets in April, Morris struck out four batters in one inning.[7][8] He finished the season 4-1--leading the league with 16 saves, a 0.63 ERA, 3.0 hits per 9 innings, 14.1 strikeouts per 9 innings, and a 0.719 WHIP—in 57 innings with 89 strikeouts over 41 appearances.[9][10] He was named an SAL mid-season and post-season All Star, a 2014 MiLB Organization All Star, and a 2014 Baseball America Low Class A All Star.[11]
Morris began the 2015 season with the St. Lucie Mets of the Class A-Advanced Florida State League (FSL), for whom he was 0–1 with a 1.69 ERA in 32.0 innings, and was a mid-season FSL All Star.[11] He was promoted to the major leagues on June 15.[12] He made his debut on June 18 against the Toronto Blue Jays at Rogers Centre in the eighth and allowed five runs on three hits and three walks in 2/3 of an inning; it was his one MLB appearance for the season.[13] To make room for Logan Verrett, Morris was sent to the Binghamton Mets, for whom he was 0–1 with a 2.45 ERA in 29.1 innings.[14] Between the two minor league teams, he allowed 4.1 hits per 9 innings, and struck out 11.9 batters per 9 innings.[15] He was named a 2015 MiLB Organization All Star.[11]
Atlanta Braves
On June 8, 2016, the Mets traded Morris to the Atlanta Braves for Kelly Johnson.[16] He was assigned to the Double–A Mississippi Braves on the same day. On August 12, Morris was recalled by the Braves.[17] The next day, Morris was optioned down to Mississippi.[18] On July 6, 2017, Morris was promoted to the Braves major league roster.[19] With the Braves, he was 1–0 with a 1.23 ERA in 7.1 innings.[15] His fastball topped out at 95 miles per hour, and his best pitch was a fading change-up.[20] Morris was designated for assignment on March 31, 2018.[21]
Los Angeles Angels
On April 3, 2018, Morris was traded to the Los Angeles Angels in exchange for cash considerations or a player to be named later.[22] The Angels called up Morris four days later and he pitched in the game that day.[23] He made nine appearances for the Angels, logging a 5.79 ERA with seven strikeouts across 14 innings of work. On August 15, Morris was designated for assignment by Los Angeles.[24] He cleared waivers and was sent outright to the Triple–A Salt Lake Bees on August 18.[25] Morris made 40 appearances for Salt Lake on the year, struggling to a 7.04 ERA with 45 strikeouts and 5 saves across 46 innings pitched. He elected free agency following the season on November 2.[26]
On November 6, 2019, Morris was selected by the Long Island Ducks in the New Britain Bees dispersal draft. Morris did not play in a game in 2020 due to the cancellation of the ALPB season because of the COVID-19 pandemic and became a free agent after the year. On May 17, 2021, Morris re-signed with the Ducks for the 2021 season.[28] In three starts, he threw 14 scoreless innings and struck out 17 batters.
San Francisco Giants
On June 11, 2021, Morris's contract was purchased by the San Francisco Giants organization and he was assigned to the Double-A Richmond Flying Squirrels.[29] He elected free agency on November 7, 2021.
Long Island Ducks (second stint)
On March 31, 2022, Morris again signed with the Long Island Ducks.[30] He became a free agent following the season.
Mumbai Cobras
On October 23, 2023, Morris was selected in the fourth round by the Mumbai Cobras, with the 31st overall pick, of the 2023 Baseball United inaugural draft.