Mann first played snooker aged 9, after being forced to quit football after a diagnosis of Legg–Calvé–Perthes syndrome, a rare disease which rots the hip bone in young boys. The main highlight of his junior career was winning the Junior Pot Black in 2007, beating Jack Lisowski 76–23 in the final.
In 2007/2008, Mann at aged 15 began to play in the secondary International Open Series tour with eight places on the professional snooker tour on offer to the top eight in the end of season Order of Merit. In 2008/2009, Mann was ranked 11th in the Order of Merit and 46th in 2009/2010.
For 2010/2011, the PIOS was dropped and replaced by the pro-am Players Tour Championship and an end-of season Q School became the new pro ticket events. In the PTC events, Mann managed several wins against professional players Liang Wenbo, Michael White, Dave Harold and Shaun Murphy notable casualties. He also qualified for main qualifying stages of the 2010 World Open professional ranking tournament through the Landywood Snooker Centre tournament, losing 0–3 to Ben Woollaston in round 1.
Mann was also a regular competitor in the Q School events, where several two-year tour cards were on offer to semi-finalists in each event. Mann came close the third event of the 2012 Q School to winning a tour place, lost a deciding frame to Robbie Williams. This performance however, enabled Mann to be a top up player for 2012 Australian Goldfields Open professional ranking event, where he reached the third round last 64 stage. He also played in the 2013 event via the same method, but lost 5–1 to Stuart Carrington in first round last 128 stage.
Mann won a two-year card on the professional World Snooker Tour for the 2014/2015 and 2015/2016 seasons in June 2014 after winning the 2014 EBSA European Snooker Championships, beating John Whitty 7–2 in the final. He missed the first two ranking tournaments of 2014/2015 season as this win came after the qualifying rounds of those events. He picked up his first win on the tour by edging experienced player Peter Lines 6–5 in qualifying for the International Championship. He came through a wildcard round match 6–1 against Niu Zhuang and then made a 142 break during a 6–5 win over Wang Zepeng. In Mann's deepest run in a ranking event to date he lost 6–4 to Michael White in the last 32. He was knocked out in the first round of both the UK Championship and Welsh Open. Mann saw off Alfie Burden 10–4 in World Championship qualifying and won three frames in a row, after Gerard Greene had come from 4–0 down to trail 7–6, to beat him 10–6. He required one more win to reach the biggest tournament in snooker, but lost 10–6 to Alan McManus. Mann was the world number 88 at the end of his first season on tour.
Mann defeated Zhou Yuelong 4–2 at the Welsh Open and then narrowly lost 4–3 to Shaun Murphy. At the final European Tour event, the Gdynia Open, Mann eliminated Sanderson Lam 4–3, Rhys Clark 4–3 (having been 3–0 down) and Jack Lisowski 4–2 to reach the last 16 where he lost 4–1 to Marco Fu. This performance helped him finish 45th on the Order of Merit to earn a new two-year place on the snooker tour. He qualified for the China Open, but was whitewashed 5–0 by Rory McLeod in the first round. By beating Kishan Hirani 10–7 and Matthew Selt 10–9, Mann was one win away from playing in the World Championship and he did so by edging out Dechawat Poomjaeng 10–9. The world number 74 Mann was the lowest ranked player in the event and the only debutant and he went 2–1 up early on, before struggling with his technique to lose 10–3.
After winning just two of his 11 matches before the 2016 UK Championship, Mann described his 6–3 first round victory over Kyren Wilson as a massive relief. He then beat Sam Baird 6–2, before falling 6–3 to Zhang Anda in the third round. At the Scottish Open he eliminated Baird 4–2 and Anthony McGill 4–1, but then lost 4–1 to Sean O'Sullivan. Mann reached the last 32 of an event for the third time this season when he overcame Michael Holt 4–1 and O'Sullivan 4–2 at the Welsh Open and he was defeated 4–2 by Kurt Maflin.