Morris was drafted by the New York Mets in the 10th round of the 2010 Major League Baseball draft. 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 innings. Morris played 2011 and 2012 with the Kingsport Mets. He played 2013 with the Brooklyn Cyclones. After splitting time between starting and relieving his first four seasons, Morris became a full-time reliever for the Savannah Sand Gnats in 2014. In a game against the Augusta GreenJackets in April, Morris struck out four batters in one inning. He finished the season with a 0.63 ERA in 57 innings over 41 appearances with 89 strikeouts and 16 saves. Morris began the 2015 season with the St. Lucie Mets of the Class A-Advanced Florida State League, and was promoted to the major leagues on June 15. 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. The Blue Jays beat the Mets 8-0. On June 17, 2015 Morris was sent to the Binghamton Mets to make room for Logan Verrett. Morris finished the 2015 season with an ERA of 67.50 in one game, 2/3 of an inning pitched with a WHIP of 9.000 while giving up 3 hits, 5 runs, 1 home run, and 3 walks. With Binghamton, he finished 1-0, 2.45 ERA in 23 games in 29.1 innings pitched with a WHIP of 1.091 while giving up 17 hits, 8 runs, 1 home run and 15 walks while striking out 35 batters.
Atlanta Braves
On June 8, 2016, the Mets traded Morris to the Atlanta Braves for Kelly Johnson. He was assigned to AA Mississippi on the same day. On August 12, Morris was recalled by the Braves. The next day, Morris was optioned down to AA Mississippi.. On July 6, 2017, Morris was promoted to the Braves major league roster. Morris was designated for assignment on March 31, 2018.
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. The Angels called up Morris four days later and he pitched in the game that day. He elected free agency on November 2, 2018.
On July 8, 2019, Morris was traded to the Southern Maryland Blue Crabs of the Atlantic League of Professional Baseball. On July 12, he was traded to the New Britain Bees in order to complete an earlier trade, without appearing in a game for the Blue Crabs.
Long Island Ducks
On November 6, 2019, Morris was selected by the Long Island Ducks in the New Britain Bees dispersal draft.
