Interestingly, fellow rookie right-hander Erasmo Ramirez was not among the cuts, and manager Eric Wedge said "he's in the mix" for a spot on the regular-season roster.
While Hultzen, Walker and Paxton have received much of the top-prospect hype, Ramirez has quietly gone about impressing the Mariners as a 21-year-old who rose to Triple-A Tacoma last year and then had an excellent Winter League in Venezuela.
"He's pitched very well," Wedge said. "He's a guy that we feel can be potentially a starter for us or pitch out of the bullpen and we're going to continue to look at him."
Ramirez threw three shutout innings in his first Cactus League start on Saturday against the D-backs and will get another start Thursday night against the Giants in Peoria. Wedge said the decision to give Ramirez a longer look wasn't based on his weekend showing.
"He wasn't going down. It wasn't dependent on last night," Wedge said. "He's a guy with more experience than those other guys and is a little further along."
Hultzen (No. 2), Walker (No. 3), Paxton (No. 5) and Ramirez (No. 13) are all ranked by MLB.com among the Mariners' top 20 prospects.
Also sent to the Minor League camp were: pitchers Yoervis Medina, Forrest Snow, Mauricio Robles and Scott Patterson; infielders Nick Franklin, Carlos Triunfel and Francisco Martinez; outfielders Johermyn Chavez, Chih-Hsien Chiang and Darren Ford; catcher Ralph Henriquez and designated hitter Luis Jimenez.
The moves leave the Mariners with 47 players remaining in Major League camp.
"It was an awesome experience as a whole," said Hultzen, the No. 2 overall pick in last June's Draft. "It was awesome to play with these guys and it's given me a lot of confidence I can go out and do the job. I just need to keep getting better. I realize there's a lot of work I still need to do."
Hultzen, Walker and Paxton were outstanding in their Cactus League debut on Saturday night against the D-backs, combining with Ramirez to throw eight innings of one-run ball with just four hits among them.
"It was hard to not sit there with a big smile on your face," Mariners pitching coach Carl Willis said.
But Wedge said they need more refining and that will come now in the Minor League camp.
"It's time for them to get down and get prepared for the regular season," he said. "We're getting to the point now with about 10 days of work left here before we go to Japan. We've got starters we've got to stretch out and other people we need to see with regard to making decisions.
"It's the right thing for them. That's why we're doing it, for them to go down there and continue to develop and gain experience and pitch regularly. They showed themselves very well here in camp and I'm excited to see how they progress."