The Rams announced on Monday evening that Clement, who was appointed to the role last summer, had been relieved of his duties, with academy director Darren Wassall taking over until the end of the season.
Derby are without a win in their last seven league games and lie fifth in the Championship table.
The midlands outfit - eighth last season under Steve McClaren - are currently five points behind leaders Hull and second-placed Middlesbrough, having been top themselves on Boxing Day.
Derby chairman Mel Morris said in Monday's announcement that when Clement came in "promotion this season was not the primary target".
Morris stressed that playing style and squad strength had been deemed "the priorities", and that Clement had been axed because the club had "not made enough progress" on that front under the 44-year-old former Chelsea, Paris St Germain and Real Madrid coach.
"We are grateful for the contribution Paul has made to the football club, but the time is right to make a change," Morris said.
"When Paul joined us last year we worked with him to develop a plan for the club which we asked him to embrace.
"It was clear in this plan, which was briefed to supporters, players, sponsors and all our stakeholders last summer that promotion this season was not the primary target.
"The priorities were building on the Derby way and style of football enjoyed in the past two seasons, adding depth and strength to our playing squad and developing and improving player and team performance.
"Sadly, on these measurements, we have not made enough progress and that is why we have decided to part company with Paul."
Derby, who spent considerable money on the likes of Tom Ince and record signing Bradley Johnson last summer, won 13 of their 30 league fixtures with Clement as boss.
Earlier on Monday, the club announced that Des Walker - the former defender who made over 400 appearances for their fierce rivals Nottingham Forest - had taken up a role as their academy's defensive coach.
The 50-year-old played for Forest over two spells in a career that also saw him turn out for Sampdoria and Sheffield Wednesday, as well as win 59 England caps.
One of his sons, 17-year-old striker Lewis Walker, joined Derby from Ilkeston FC last month. The other, Tyler Walker, is a forward at Forest.
Derby also revealed their former defender Craig Short had rejoined their academy staff.
The club said Short, 47, would ''provide additional coaching support to the under-21 squad'', with both men brought in initially on deals until the end of the season.
Short was Derby's head of recruitment in the academy between September 2011 and June 2013 before becoming part of the first-team coaching staff at Blackburn, another of his former clubs.