The soap star, who was partnered by Erin Boag, finished bottom of the judges' leaderboard, only scoring 22 points for his tango. Craig Revel Horwood claimed that Groves's routine was filled with "mistakes galore" and described it as "mechanical".
Groves, who was in the bottom two for the third consecutive week, was joined in the dance-off by Laila Rouass and Anton Du Beke. Rouass totalled 29 points for her waltz.
All four judges chose to save Rouass and Du Beke without hesitation. Afterwards, Erin Boag praised Groves, calling him the perfect partner.
The actor added: "I've met Rod Stewart, I've met Shirley Bassey and most importantly I've met Erin Boag, so thank you very much."
Earlier in the evening, Olympic long-jumper Jade Johnson and Ian Waite pulled out of the competition following her knee injury last Saturday.
Next Saturday, the remaining five celebrities will dance either a rock 'n' roll or a Charleston routine.