Ruth Brown, Adam Isaac and Leanne Mitchell received enough votes from the viewing public to continue onto next week's live show for Jones's team.
Meanwhile, Tyler James, Jaz Ellington and Frances Wood were also voted through to the next round for Team will.i.am.
Buttery faced off against duo Matt and Sueleen after receiving the least amount of votes from the public for Team Tom Jones.
Jones decided to pick the couple over Buttery, saying: "They're both great entertainers. It's very difficult because they're so different. I can only judge it on last night's performance, and I think I'm going to take Matt and Sueleen."
A tearful Buttery praised his coach, saying: "I hope that people won't be losing me. This isn't the end for me, I've loved working for Tom.
"Obviously I'm gutted and it feels like my heart has been ripped out, but I'm still happy."
Jones added: "I feel as sad about it as Sam does, it was a hard decision. I only went on last night's performance. You're a great talent and more strength to you. Somebody had to stay and somebody had to go. It was not an easy thing."
will.i.am was next to choose which act to save, and he decided to send home 17-year-old Sophie Griffin over Joelle Moses.
He explained: "I never really never liked talent shows, but this show is special because every single person actually sings really, really good. So I'm proud of being on the show.
"This is the hardest thing because both you guys are amazing talents. Sophie, you're special, you've learned so much. It took me freakin' ten years to learn what you learnt in two months.
"I promise you, me and Dante and Apl are going to be there for you whatever you need. But for the show, I'm gonna take Joelle."
Griffin responded: "I couldn't have had a better coach. It's been a dream come true."
The Voice UK will continue next week when Team Danny O'Donoghue and Team Jessie J will perform live for the first time.
The next live show will air on Saturday (May 5) at 7.10pm on BBC One.
Photo gallery: The Voice live shows week one results show: