MESA, Ariz. — As the A’s continue to add a player to camp nearly every day — catcher Nick Hundley to start, left-hander Brett Anderson on Wednesday, outfielder Robbie Grossman any day now — Thursday’s new man presented some confusion.

Oakland signed left-hander Tyler Alexander to a minor-league deal with an invite to big-league spring training. But ... which one?

There are two. One plays in the Tigers’ system, and the other has kicked around independent ball, Mexico and the Dominican Republic.

“I don’t know if he gets confused as much as I do for him,” the latter said at Hohokam Stadium. “Playing in Mexico and the DR, people come up to me all the time asking me to sign a card and I give them the same answer: ‘I know it’s not me.’ Because I probably have one or two cards out there and they’re indie-ball cards. I’m like, ‘That’s the Tigers guy, not me.’ It kind of sucks, but it is what it is.”

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Alexander, 27, has spent the past four years trying to work his way back from two drug suspensions, both for testing positive for marijuana. The second positive test came when he was playing independent ball in 2016 and the penalty was three years.

“I’m not trying to hide it,” Alexander said of his suspensions, the first of which came when he was 22 and in the Brewers’ system. “I’ve had it over my head for a long time — I couldn’t sign with any teams until we petitioned to have it lifted and MLB gave me the OK.”

The A’s also had to wait until Alexander’s Mexican League team, Quintana Roo, released him, but once he was free, the A’s viewed him as an intriguing and low-risk option, a lefty who can start and pitch in relief.

“He has certainly persevered,” A’s assistant general manager Dan Feinstein said. “Obviously, we believe in his ability enough to bring him into big-league spring training.”

Feinstein described Alexander as having a crossfire, deceptive delivery and a fastball that registers in the low 90s that he can cut and sink, plus a slider and a changeup. “Everything is down,” Feinstein said. “Everything is around the zone.”

That part is relatively new, Alexander said. When he was in the Brewers’ system, he struggled with his control.

“I learned how to throw strikes,” he said. “I give a lot of credit to my pitching coach, Michael Schlact. He’s now the manager in Fargo, where I started in indie ball. He worked with me on the mental side of the game. ... I learned my body, I learned myself and I cut the walks in half. The game changes when you throw strikes.”

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Alexander says the delivery is a little funky, somewhat reminiscent of Chris Sale’s. “When you see me, you’d assume I don’t throw strikes,” he said.

The A’s have added three left-handed pitchers since the start of the month in Anderson, Alexander and reliever Jerry Blevins, who — like Alexander — is on a minor-league deal. Other left-handed options among the minor-league invitees include Dean Kiekhefer, Wei-Chung Wang, Kyle Lobstein and Kyle Crockett.

“We went from a position the last couple of years where we haven’t had a whole lot of left-handed relievers to quite a few to choose from,” manager Bob Melvin said, adding that Feinstein mentioned to him that Alexander “is someone they had their eye on for a couple of years.”

Alexander is enormously appreciative. He was willing to put in the time playing wherever was necessary, but he wasn’t sure he’d even get back to a big-league organization.

“I kind of counted it out, I didn’t think it was a possibility anymore with the off-the-field stuff,” Alexander said. “I’m just happy that these guys gave me the opportunity to keep chasing the dream.”

Susan Slusser is a San Francisco Chronicle staff writer. Email: sslusser@sfchronicle.com Twitter: @susanslusser