The former EastEnders actress and partner Andrei Lipanov lost out in the skate-off to model Melinda Messenger, who was saved by a unanimous judges' vote.
Earlier, Bissix had failed to impress the judges with her routine to Celine Dion's 'The Power Of Love', scoring 13 out of a possible 30 points.
Robin Cousins said: "It was an okay start, it wasn't a good start."
Ruthie Henshall praised her "determination and drive", but added: "You need to work on your nerves, become much more solid. And grace - that's the word of the day."
Leaving the ice, Bissix said: "I'm coming back every week. I'm gutted, I just wanted to do another routine.
"I've done seven weeks of training and I have never stepped on the ice [before that] so for that I am proud of myself."
Former Liberty X singer Jessica Taylor finished at the top of the leader board, scoring 21 out of 30.
Last week, ex-footballer Graeme La Saux became the first man to be voted off the show.