Mutumbami was named in the 21-Member squad for the Bangladeshi tour in April 2013. He made his test debut against Bangladesh in April 2013. He scored a quick-fire 11 runs 13 balls with 2 fours and took his first dismissal as wicketkeeper in both international cricket and Test cricket catching Nasir Hossain off Kyle Jarvis in the Bangladesh's first innings.
Although he was out for a first-ball duck in the second innings, he had a better show behind the stumps catching Jahurul Islam off Shingi Masakadza and stumping Sohag Gazi off Graeme Cremer, his first stumping in both International and Test Cricket. Zimbabwe went on to win the test by 335 runs.
In the second test, Mutumbami took two catches in the Bangladeshi innings. In the Zimbabwean first innings he went on to take his current career best of 42 runs 72 balls 3 fours and a six. He had an 85 run stand with Elton Chigumbura. In Bangladesh's Second Innings he took three catches and a stumping but scored 12 when he came out to bat again and Zimbabwe lost the Match by 143 runs.
In August 2014, Mutumbami made 73 for Zimbabwe A in the second tour match against Afghan because of these he was included in Zimbabwe ODI squad for last two ODI against Afghanistan. He scored 64 runs on his debut in 100 runs lost against Afghanistan at Harare Sports Club.
Mutumbami opened in the three ODIs against South Africa, but only made scores of 13, 12 and 0, after which he was moved down to No.7 for the game against Australia. He did not find much luck there either making only 11 as Zimbabwe's need to bulk up their batting grew more pressing and was ruled out after being hit by a ball during nets and he sustained a hairline fracture to a bone in his right forearm.[8]
Mutumbami was included in the ODI series against Afghanistan, and returned to opening the batting. He was not successful in first two games, but in the third ODI, he scored 74 from 92 balls, helping the team to victory and lead the series 2–1.[9][10]
In September 2018, he was named in Zimbabwe's squad for the 2018 Africa T20 Cup tournament.[11]