Payamps signed with the Colorado Rockies as an international free agent on May 1, 2011.[1] He spent his first two seasons with the DSL Rockies, going 1–3 with a 3.29 ERA in 38 innings in 2011 and going 1–2 with a 3.02 ERA in 59.2 innings in 2012. Payamps spent 2013 with the Grand Junction Rockies, going 4–7 with a 6.06 ERA in 68 innings. He played for the Tri-City Dust Devils in 2014, going 0–2 with a 6.10 ERA in 20.2 innings.[1]
In 2015, Payamps was released by the Rockies on May 6 and did not appear in any professional games during the season.[1]
Arizona Diamondbacks
Payamps signed a minor league contract with the Arizona Diamondbacks on November 30, 2015.[1] He returned in 2016 and split the season between the Kane County Cougars and the Visalia Rawhide, going a combined 10–8 with a 3.86 ERA in 132.1 innings. His 2017 season was split between Visalia, the Jackson Generals, and the Reno Aces, going a combined 11–7 with a 4.30 ERA in 150.2 innings. He split the 2018 season between Jackson and Reno, going a combined 9–8 with a 3.87 ERA in 116 innings.[1] The Diamondbacks added Payamps to their 40-man roster after the 2018 season.[2]
Payamps opened the 2019 season back with Reno.[3] He suffered a broken foot on April 6 when he was hit by a batted ball.[4] He finished the 2019 minor league season posting a combined 5–6 record with a 3.89 ERA in 78.2 innings between Jackson and Reno.
On August 17, 2019, the Diamondbacks promoted Payamps to the major leagues.[5] He made his major league debut on August 21 versus the Colorado Rockies, allowing two runs over three innings pitched.[6] With the 2019 Diamondbacks, he appeared in two games, striking out three batters in four innings pitched while allowing two earned runs.[7] In 2020, he again appeared in two games with the Diamondbacks, striking out two batters in three innings, while allowing one earned run.[7] Overall with Arizona, Payamps appeared in four MLB games, pitching to a 3.86 ERA in four appearances without a decision.[7] On November 20, 2020, Payamps was designated for assignment.[8]
Toronto Blue Jays
On November 25, 2020, Payamps was claimed off waivers by the Boston Red Sox.[9] On February 3, 2021, he was designated for assignment after the signing of Garrett Richards was made official.[10] On February 10, Payamps was claimed off waivers by the Toronto Blue Jays.[11] On February 22, he was again claimed off waivers by the Red Sox.[12] On March 6, Payamps was again claimed off waivers by the Blue Jays.[13] Payamps recorded a 2.70 ERA in 22 appearances with the Blue Jays, but was designated for assignment on July 16.[14]
Kansas City Royals
On July 21, 2021, Payamps was traded to the Kansas City Royals in exchange for cash considerations.[15] On August 18, 2022, Payamps was designated for assignment.