On the one-year anniversary of their deal for a franchise quarterback, the 49ers were dealing with far different news at the NFL’s most important position Tuesday.

Two days before their prime-time meeting against the Raiders, quarterback C.J. Beathard was struggling to grip a football because of a sprained right wrist and didn’t practice. If Beathard can’t play, Nick Mullens, a 2017 undrafted free agent who has not taken a regular-season snap, would make his debut for a 1-7 team on a six-game losing streak.

“C.J. would be good if we were playing on Sunday,” head coach Kyle Shanahan said, “but it’s going to be a test for Thursday — and we probably won’t know until then.”

Beathard spoke to reporters while sporting a wrap that covered his wrist and part of his hand. He said X-rays confirmed he did not break any bones after he hit his arm on a helmet during the second quarter of an 18-15 loss to the Cardinals on Sunday. Beathard said he dealt with discomfort during the game, but adrenaline was a reason his wrist issue didn’t affect his ability to throw.

“My wrist and thumb are kind of messed up,” Beathard said. “It’s two days after the game, so hopefully tomorrow it will feel a lot better.”

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A year ago, the 49ers were 0-8 but had some hope after they unexpectedly landed New England backup Jimmy Garoppolo for a second-round pick. On Tuesday, with Garoppolo on injured reserve, their QB situation went from compromised to potentially catastrophic, as Beathard’s injury increased the odds they’ve yet to reach rock bottom in 2018: A loss to the Raiders (1-6), who are in the midst of a roster purge, would represent a nadir.

In the preseason, Mullens completed 31 of 43 passes for 396 yards with a touchdown and three interceptions.

“Nick’s a very smart guy who works at it nonstop,” Shanahan said, “and he’ll be able to go in there and execute the offense. He knows what he’s doing.”

If Mullens starts, his backup would be Tom Savage, who originally was signed Oct. 16. Savage, 28, is a 2014 fourth-round pick who has made nine career starts, but he’s early in the process of absorbing the playbook. Last year, Garoppolo made his first start for the 49ers nearly five weeks after he was acquired.

Shanahan indicated the 49ers would use just a portion of their game plan if Savage was forced into action.

“He’s three weeks into it,” Shanahan said. “… The whole offense and everything that would have to be limited because that’s too much for a guy to learn in this amount of time.”

At Southern Mississippi, Mullens broke Brett Favre’s school records for passing yards (11,994) and touchdowns (87) and was Conference USA Player of the Year as a junior. He put up those numbers in a spread offense, where he was in a shotgun formation.

Shanahan said 49ers quarterbacks coach Rich Scangarello interviewed Mullens before the 2017 draft. During their talk, Scangarello asked Mullens how he prepared to play in the Senior Bowl, where he had to take snaps from under center.

“He had to look up on YouTube how to do drops and stuff under center because he was always in (shotgun) throughout college,” Shanahan said. “But that’s the kind of guy he is. He’s going to figure it out.”

Said Mullens, smiling: “I think that story — they took it and ran with it,” Mullens said, adding, “You’ve got to be able to adapt, and that’s kind of what I’ve done.”

On Tuesday, as Mullens spoke, it remained to be seen whether Beathard’s injury would mean he would adapt to a new role Thursday night.

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch