Donohue was born in Bodedern on Anglesey and played with Bodedern Athletic before joining Everton. He spent six years at Everton's academy and was unable to gain a professional contract. He returned to North Wales and played amateur football with Porthmadog, Holyhead Hotspur and Caernarfon Town. In 2014, he moved to the English non-league with Sutton Coldfield Town. Donohue scored his first goal for Sutton on 27 September 2014, netting the first through a penalty kick in a 2–0 home win against Kidsgrove Athletic. He made 37 appearances for the club, as his side achieved promotion to Northern Premier LeaguePremier League through the play-offs.
Chesterfield
Donohue went on trial at Chesterfield in the summer of 2015 and was able to earn a contract. He made his professional debut on 12 September 2015 in a 3–3 draw against Colchester United. Donohue signed a contract extension on 10 August 2016, keeping him at the club until 2018. Donohue scored his first professional goal on 14 March 2017, netting the equalizer in a 3–3 home draw against Peterborough United. In May, he was awarded the Players' Player of the Year.
Portsmouth
On 18 August 2017 Donohue joined fellow League One club Portsmouth on a two-year deal for an undisclosed fee. He made his debut eight days later in a 1–1 draw at Wigan Athletic, being substituted after 53 minutes. On 17 October, he was sent off in a 2–1 loss at Doncaster Rovers for violent conduct towards Niall Mason, but Portsmouth successfully appealed against his three-game suspension. Donohue played less frequently in 2018–19. In his first game, away to Crawley Town in the EFL Trophy on 9 October, he scored the only goal of the game, his first for Pompey. He was released on 17 May 2019.
On 9 July 2019, Donohue joined League Two side Mansfield Town on a two-year deal. He arrived not fully recovered from injury and made his debut in the EFL Cup first round match against Morecambe on 13 August, being substituted at half time because of his condition as the team lost on penalties after a 2–2 home draw. On 19 August 2019 Donohue and Mansfield teammate Jacob Mellis were suspended by the club for "an alleged serious breach of club discipline". Following a club disciplinary investigation his contract was terminated on 2 September.
On 12 October 2019, Donohue joined League Two side Swindon Town on month-by-month contract. He made his debut the same day in a 1–1 home draw with Plymouth Argyle, and after the game manager Richie Wellens said that the Robins had tried to sign him in the summer. As his second month was not registered in time with the EFL, he was then barred from playing again until 2 January. Swindon did not negotiate to sign Donohue when January came, with Wellens saying that this was due to the player's injury, rather than his court proceedings.
In January 2012, Donohue pleaded guilty at Caernarfon Magistrates Court to a charge of assaulting a woman at a nightclub in Bangor, Gwynedd, the previous 13 November. He was fined £500 and £85 court fees, and sentenced to 120 hours of community service and four weeks of curfew. In January 2020, Donohue pleaded guilty at Nottingham Crown Court to charges of assault, affray and grievous bodily harm committed in Mansfield the previous 16 August. Donohue has one son, Mason Donohue, who was born in 2018 at Queen Alexandra Hospital in Portsmouth.
