His clean 90.13sec second round time was second only to Czech paddler Tomas Zima, who clocked 88.04 to lead qualifying.
"I had a good first run and thought it went pretty well but when I got to the bottom, I saw I'd picked up a 50.
"It was a bit of a surprise because I thought I'd left myself enough but I left it up to the judges.
"My second run was heaps better - I felt really good and managed to get the second-fastest time overall, so I'm really looking forward to the semis to see how I go," Mutton said.
There was also plenty of drama for under-23 paddlers Finn Butcher, of Alexandra and Tauranga's Callum Gilbert, who both picked up penalties in their first run but were comfortably inside the top-30 that automatically qualified for Friday's semifinals.
Gilbert clocked 93.92sec, with one two-second penalty for a touch on gate 15, to qualify in 21st, while Butcher was two places further back after hitting gate 12 and finishing in 94.34.
France's Mathieu Desnos was the fastest under-23 qualifier in 84.06, ahead of Germany's Stefan Hengst in 84.56, with another Frenchman Pol Oulhen, third in 86.13.
The other under-23 New Zealand kayaker Alex Hawthorne missed a gate in his first run but raced clean in the repechage, finishing 14th and missing the semifinals by just one second.
Kiwi Callum Aitken just missed qualifying in his second run, finishing 14th, while Damian Torwick agonisingly missed the final gate in both his runs to drop out of contention.