Born in Derby, Derbyshire,[1] Groves began his career in non-League football, playing for Belper Town before joining Burton Albion in 1988 for whom he appeared at Wembley Stadium for in the 1987 FA Trophy Final.

[1] Having not made the grade at Filbert Street, Leicester placed Groves on the transfer list and he eventually left the club in January 1990.

Groves became part of a nostalgic playing squad that harboured such professionals as Ivano Bonetti, Steve Livingstone, John McDermott and Gary Croft.

Whilst at the club Groves also played under Brian Laws, and caretaker manager John Cockerill His next port of call was to join West Bromwich Albion for £600,000 in 1996 where he was signed once again by Alan Buckley.

Groves would be part of a selection of players who transferred between West Brom and Grimsby in the late to mid nineties through the Alan Buckley connection.

On the last day of the 2000–01 season, Groves scored a 25-yard goal in the 26th minute to win 1–0 over promoted Fulham, which secured their place in Division One.

He was sacked in 2004 but despite being relinquished of his managerial duties, Groves remained on as a player until he was jettisoned by the club's incoming new manager.

[6] Groves signed a one-year contract with York City, who had recently been relegated to the Conference National, in June 2004 along with former Grimsby teammate Kevin Donovan.

He brought his 19-year playing career to a close in May 2006 after helping them to promotion to the Conference National after making 32 appearances and scoring five goals in the 2005–06 season.

He brought back former player Graham Rodger as his assistant and bolstered his side with several good loan signings, including Charlton Athletic duo Andy Todd and Martin Pringle.

Groves managed to steer the club to safety and secured Town's place within what is now the Football League Championship for another year.

[14] On 25 March 2012, following the dismissal of Lee Bradbury, he became joint-caretaker manager of Bournemouth with head of youth Shaun Brooks, until the end of the 2011–12 season.

[24] On 20 April 2017 new Birmingham City manager Harry Redknapp appointed Groves as first-team coach, reuniting the pair whom had worked together at Portsmouth.

[26] On 9 July he was named as John Gregory's assistant for Indian Super League side Chennaiyin FC.

[31] In August 2022, Groves moved to Indian Super League club NorthEast United as an assistant to Israeli head coach Marco Balbul.