Sitting as a member of the Victorian Legislative Assembly, Groth represents the Liberal Party in the seat of Nepean.

Groth and Andrew Kennaugh of Great Britain lost in the finals of the 2005 Wimbledon boys' doubles championship to Jesse Levine and Michael Shabaz 6–4, 6–1.

[4] In 2012, in an ATP Challenger in Busan, Groth hit the fastest serve on record with a 163.4 mph (263.0 km/h) ace, but lost the match to Uładzimir Ihnatsik, 4–6, 3–6.

On 8 January, Groth was awarded a wild card into the 2014 Australian Open,[6] but lost in round one to 28th seed, Vasek Pospisil in straight sets.

In March, Groth qualified for Indian Wells Masters, but lost in round 1 to Mikhail Kukushkin, 4–7 in the third set tie-break.

In June, Groth made the final of the 2014 Aegon Nottingham Challenge but lost to compatriot Nick Kyrgios 6–7(3–7), 6–7(7–9).

Groth made his Wimbledon debut after winning his way through qualifying, but lost in round 1 to Alexandr Dolgopolov in three sets.

Groth entered the Hall of Fame Tennis Championships, where he reached his maiden ATP semi-final, defeating defending champion Nicolas Mahut in the quarter-finals.

[7] In August, Groth won his first Grand Slam match, defeating Albert Ramos Viñolas 6–3, 7–6(7–5), 6–3 in the 2014 US Open.

In February, Groth headed to North America and lost in round 2 of Memphis to eventual runner-up Kevin Anderson.

Groth started his grass court season at the Manchester Challenger where he reached the final and defeated compatriot Luke Saville to win the title.

In this 3rd round match, he made the second fastest serve ever at the Wimbledon tournament (147 mph), and was the only player to take a set off of Federer until the final, losing to the 7-time champion 4–6, 4–6, 7–6(7–5), 2–6.

Groth then replaced Nick Kyrgios to play Mikhail Kukushkin where he defeated him in 4 sets to level the tie at 2–2.

Groth next contested the Bogotá Open as the 6th seed where he defeated Guido Pella before losing to former world number 8 Radek Štěpánek in straight sets.

Groth next played at the 2015 Winston-Salem Open and defeated Jared Donaldson before losing to eventual semi-finalist Steve Johnson.

At the Australian Open, Groth defeated Adrian Mannarino before losing to number 2 seed Andy Murray in the second round.

Groth played for Australia in Davis Cup World Group losing his singles match to John Isner in straight sets.

Groth had a last minute call-up to represent Australia at the 2016 Summer Olympics in Rio de Janeiro, but lost in the first round to Belgium's David Goffin.

Groth commenced the 2017 with a wild card into the 2017 Brisbane International, where he defeated Pierre-Hugues Herbert before losing to Dominic Thiem in round 2.

Groth lost in round 1 of the 2017 Australian Open to Steve Darcis, but paired with Chris Guccione to reach the quarter-final of the doubles, losing to eventual champions Henri Kontinen and John Peers.

In February, Groth was selected to play in round 1 the 2017 Davis Cup against Czech Republic, he paired with John Peers to win the doubles taking Australia to an unbeatable 3–0.

[13] Groth won the three-candidate contest with seventy-four votes (67%), compared with runner-up David Burgess' thirty-three, and former Bentleigh MP Elizabeth Miller with four.

I'm confident, if we are to have any chance tonight of the Liberal Party and the Coalition getting into government in this state, Nepean is the one that has to turn.

This move was criticised by moderate members of the party, with one senior Liberal saying “it spoke volumes about Mr Groth that he had decided to tell the media before his colleagues”, while another described him as a “wanker”.