The 18-year-old Auger-Aliassime, the youngest player in the world's top 100 and ranked a career-high 21st, will face Matteo Berrettini in Sunday's final.
Italian Berrettini beat home hope Jan-Lennard Struff 6-4, 7-5.
Auger-Aliassime, who missed the recent French Open with a thigh injury, will be aiming for his maiden ATP title after final losses in Rio de Janeiro and Lyon this year.
He beat German Dustin Brown in a thrilling quarter-final on Friday in a deciding-set tie-break, saving a match point.
"It's been an unbelievable week for me," Auger-Aliassime told atptour.com. "I've been playing good tennis. I got through on the edge yesterday and to be in another final, it's unbelievable.
"So I think I'll try to enjoy it and give everything also because it's obviously my third final this year, so I'll try to give it my all to maybe get my first title."
The grass-court event in Stuttgart serves as a warm-up for Wimbledon, where Auger-Aliassime will be playing in the main draw of a Grand Slam tournament for only the second time.
Results from the ATP tournament in Stuttgart on Saturday (x denotes seeding):
Felix Auger-Aliassime (CAN x7) bt Milos Raonic (CAN x6) - walkover
Matteo Berrettini (ITA) bt Jan-Lennard Struff (GER) 6-4, 7-5