Karina Smirnoff -- Carted Off 'DWTS' Set ... With Multiple Injuries

Karina Smirnoff went down so hard during a "Dancing With the Stars" rehearsal ... she had to get lifted onto a stretcher and rushed to the hospital.

TMZ obtained video of EMTs whisking Smirnoff away after she bit it in practice ... suffering knee and wrist injuries. Watch the video ... Karina's clearly in pain, and her wrist is already wrapped up in an ice pack.

Sources close to the show tell us x-rays show she didn't fracture anything, but just in case ... producers are scrambling to find a replacement. Karina's already been voted out, but she still performs in each show.