Mentel-Spee, 41, from the Netherlands, has been the dominant figure in the sport all season and maintained her dominance at Rosa Khutor.
She finished over nine seconds clear of France’s Cecile Hernandez-Cervillon.
Strong led home an American clean sweep of the men’s medals ahead of team-mates Michael Shea and Keith Gabel.
The 27-year-old finished in one minute 43.61 seconds, 0.57 seconds clear of Shea and 3.57 seconds ahead of Gabel.
The competition saw athletes, who all have lower limb impairments, race individually down the course and negotiate rollers and jumps.
Mentel-Spee was a six-time Dutch national champion in halfpipe and snowboard cross events and was aiming to qualify for the 2002 Winter Olympics in Salt Lake City when she was diagnosed with cancer and had to have her lower right leg amputated.
But she returned to the slopes four months after the operation and became the sport’s first world champion last year.
Strong, who was brought up in Hawaii, was a former professional skateboarder but in 2004 he was hit by a car while riding his motorbike and had his left leg amputated below the knee.