McDonald had the surgery on May 20, the day after doctors discovered what he described as a "little bump" during a team physical.
McDonald, who spent most of Wednesday's minicamp on a stationary bicycle, is expected to be ready to compete fully once training camp begins in Spartanburg, South Carolina, on July 26.
"It was obviously surprising," McDonald said after Wednesday's practice. "I just kind of made up my mind not to get down, not to let it affect me, as much as I could.
"Just stay positive, and obviously it's worked out. Thank God for that."
Doctors told McDonald they caught the cancer before it spread.
McDonald was signed to Carolina's practice squad on Oct. 21 after being waived by the Dolphins in August. He later was identified as "Player A" in the Wells report on harassment in the Miami locker room involving Jonathan Martin and Richie Incognito.
In the report, McDonald was named as a player who was a target of harassment. The report said former Dolphins offensive line coach Jim Turner gave McDonald a male blow-up doll as a Christmas gift in 2012, the player's rookie season.
McDonald's agent, Brett Tessler, sent out a statement on behalf of his client earlier this year that said: "While Andrew can't speak for other players involved in the report, he personally has had no problem with the Miami Dolphins organization and has the highest opinion of Coach Turner both personally and professionally and feels terrible about the way their relationship has been portrayed in the report."
McDonald made his first public statement on the report on Wednesday.
"Obviously, we went through a lot, you know, and everybody kind of goes through an adjustment getting into the league," he said. "I just kind of saw it as rookies -- picking on the rookies and stuff, just playing around, messing with them.
"But some people, it goes a little too far sometimes. That's pretty much all I want to say about that."
Asked whether he ever thought things went too far, McDonald said, "I don't think I really want to get into that really."