The champion ski racer landed in the bottom two when public votes and judges' scores were combined for a fourth week, this time facing off against Chico.
After the skate-off, panelist Katarina Witt declared that the decision to eliminate one of them was "very difficult", but ultimately chose to save Alcott.
However, Louie Spence tied up the vote by giving his backing to Chico, and Robin Cousins sent Alcott home after declaring that her opponent still "had that spark" about him.
As Chico fell to his knees in relief, Alcott skated over to hosts Phillip Schofield and Christine Bleakley for her exit interview.
"I feel gutted because I love this competition," she admitted. "But everyone's a lovely skater out there and I've just had so much fun."
Alcott then dedicated her Dancing on Ice stint to "everyone out there who's overcome adversity", saying that she couldn't have imagined competing on the show after fracturing her leg in a skiing crash in December 2010.
"This time last year I was on crutches, I couldnt walk and now I've done this," she beamed.
Chico, Jennifer Ellison, Matthew Wolfenden and Jorgie Porter are left to compete in next week's semi-final, which will see them take part in a solo skills test. It was also announced that the contestant who finishes top of the leaderboard will automatically progress to the final.
Dancing on Ice continues Sunday (March 18) at 7pm on ITV1.