Mennie grew up in Coffs Harbour, New South Wales, but as a teenager he moved to Nelson Bay. While living in Nelson Bay he played cricket for grade cricket club Western Suburbs in nearby Newcastle. At the time he played as a batting all-rounder, but once his body matured he became a specialist fast bowler. At the age of 17 Mennie moved back to Coffs Harbour and quickly broke into both the New South Wales Country Colts team and the Western Suburbs District Cricket Club in Sydney Grade Cricket. In 2010 he also broke into New South Wales' Second XI, but he saw that he would have limited opportunities to play for the state team, so in 2011 he moved to Adelaide to play for Adelaide University Cricket Club and he was given a rookie contract with South Australia's state team.

In October 2011 he made both his List A and first-class cricket debuts for the Redbacks. His first big haul came against Western Australia when he took figures of 7/96, including the last five wickets of the innings to bowl out Western Australia and keep the Redbacks in the game. He took the second-most wickets by a South Australian for the Sheffield Shield season with 23 wickets at an average of 26.26. He was signed to the Perth Scorchers in the Big Bash League Twenty20 competition, along with Ryan Duffield in December 2011 to replace the injured Mitchell Johnson and Mark Cameron. However, he didn't make his Twenty20 debut until October 2012, when he played in the Scorchers opening match against the Titans in the 2012 Champions League Twenty20.

In the 2012–13 Sheffield Shield season Mennie improved on his form from the previous season. His best performance was 6/43, helping the Redbacks to bowl out Victoria cricket team for just 136 runs. He became the fourth-highest wicket taker in the competition with 33 wickets at an average of 22.03 despite only playing six matches. Mennie also proved his usefulness as a lower order batsman with a score of 79 not out, his maiden first-class half-century, against Queensland. He followed up less successfully in the 2013–14 Sheffield Shield season with only 19 wickets and went into a lull for the next couple of season. He wasn't in good form in Twenty20 cricket either and changed teams from the Scorchers to the Hobart Hurricanes.

Mennie came back into the spotlight in the 2015–16 Sheffield Shield season. Despite not having any five-wicket innings for the entire season, he led