French fourth seed Mahut could only reach the quarter-finals at Newport before suffering a 6-3 6-4 loss to world number 123 Groth.
Big-serving Groth only put in 54 per cent of first serves and seven aces, but Mahut was still unable to find answers at the ATP 250 event played on grass.
The Australian broke serve in the sixth game of the opening set and had another chance in the eighth, but one was enough as Mahut won just five return points.
Groth dominated the second set and grabbed a break in the third game before needing four match points to seal his win.
"I've had a great grass-court season already. I really had nothing to lose," Groth said.
"I've got myself in great shape," Groth said.
"I'm not losing my mind out on court. I'm doing a lot of things better. I've tightened up my groundstrokes. I'm volleying better than I ever have. I'm making it tough for guys to break me. I'm becoming more prepared to be a top player."
Croatian second seed Karlovic also used his powerful serve to see him into the semi-finals as he beat Israeli Dudi Sela 7-6 (7-3) 7-5.
The result continued Karlovic's dominance of Sela as he made it six wins in as many matches between the pair.
Both players squandered a break point in the first set and when Sela fell behind early in the tie-break, there was no way back.
As the second set also looked headed for a tie-break, Karlovic broke in the 12th game to set up a meeting with Groth.