The brother of senior star Adrian got the key scores to set up a final against neighbours Tipperary, with the Cats now one game away from a first All-Ireland minor title since 2014.
After Mullen’s opening point, Kilkenny struck a remarkable 10 wides in a row across the next 15 minutes.
Clare blitzed 2-3 in that spell to lead by eight, with goals for their first two scores via a Conor Ralph rebound and Paul Rodgers’ strike.
Kilkenny’s wides included a 10th-minute Mullen penalty miss after Ollie O’Donovan had been chopped down by McNamara.
They settled with a goal when Conor Holohan bounced the sliotar through the keeper’s legs to make it a one-score game. Ralph’s pair pushed Clare 2-6 to 1-4 ahead at half-time.
Mullen was brought out the field and his six points drew the sides level by the three-quarter mark as Clare’s wide tally rose into double-figures.
In the 47th minute, they moved ahead. Eoghan Cahill and O’Donovan both saw efforts blocked before the latter found the bottom corner at the third attempt for a 2-11 to 2-8 lead.
They led by four as late as the 58th minute but Clare kept running at them and reeled off points from Darragh McNamara and Harry Doherty (0-3) to level.
Kevin Buggy looked like he had won it but Rodgers equalised again in the final seconds of the four added minutes to make it 2-15 apiece and trigger extra-time.
Kilkenny rebuilt their four-point lead with scores from Mullen (0-2), Buggy, and an incredible Patrick Lacey effort. It went from bad to worse for Clare when Rodgers received a straight red card for an off-the-ball incident at the end of the half with the scoreboard reading 2-20 to 2-16.
Matthew Corbett struck three frees but Kilkenny held on with scores from Mullen, Robbie Doherty, and Lacey’s second.
Scorers – Kilkenny: J Mullen 0-13 (9f); O O’Donovan, C Holohan 1-0 each; R Doherty, B McDermott 0-3 each; K Buggy, P Lacey 0-2 each. Clare: H Doherty 0-7 (4f); C Ralph 1-2; M Corbett 0-5 (5f); P Rodgers 1-1; D Kennedy, J Cullinan, P Finneran, D McNamara, J O’Connor 0-1 each.
Kilkenny: J O’Doherty; O Henderson, L Phelan, B Brennan; D Barcoe, J Dollard, M Rohan; K Buggy, E Brennan; R Doherty, B McDermott, C Holohan; O O’Donovan, J Mullen, J Cody. Subs: L Raggett for Dollard (12-h-t, blood), Raggett for B Brennan (h-t), E Cahill for Cody (38), C Byrne for McDermott (58), P Lacey for E Brennan (58), C McEvoy for Holohan (73), A Clifford for Cahill (73), D Behan for Barcoe (79, inj).
Clare: M Crotty; S Óg Kilkenny, S McNamara, D Moroney; R Mulcahy, J Cullinan, D Kennedy; G Ball, M Corbett; P Finneran, T Lohan, H Doherty; C Ralph, P Rodgers, L Murphy. Subs: R Hayes for G Ball (41), D McNamara for Lohan (45), D Ball for Corbett (52), J O’Connor for Ralph (53), M Vaughan for Finneran (60), Finneran for Vaughan (66), E Crimmins for Kennedy (h-t e-t), Corbett for Finneran (h-t e-t).
Referee: C Cunning (Antrim).