“Jeez, dad… shut it!” the 45-year-old actor said in a videotaped interview with Radar that the site said was recorded Saturday.
Also read: Charlie Sheen: Joking Aside, Is He Mentally Ill?
“Okay, Pop, walk through a cancer ward right now and find any of those mother f—ers who look like me,” he added.
The site said Sheen also accepted its challenge to take numerous drug tests, and passed.
The interview was just one of many Sheen has given recently. Sheen has an appearance on ABC's primetime news program "20/20," scheduled to air Tuesday night, and also sat down for NBC's "Today" for a spot that will run Monday.
Also read: Martin Sheen Compares Son's Addiction Fight to Cancer
The producers of "Today" sent out the following tweet Sunday: "Charlie Sheen demands personal apology from 2 1/2 Men producer & CBS."
In a "20/20" promo, Sheen said, "I have one speed, I have one gear, go. And I dare anyone to keep up with me."
He also stated: "I am on a drug, it's called Charlie Sheen."
Here's the promo:
Sheen went off on Chuck Lorre, the creator of the CBS hit comedy, in radio interviews last week, and the network and Warner Bros. TV subsequently shut it down for the season. But before that happened, Sheen gave yet another interview, this one to GQ's Amy Wallace.
Wallace also interviewed Sheen pals, porn actress Kacey Jordan and Sean Penn.
Here are some excerpts from the issue, which will hit newstands March 22:
>> Discussing his latest drug binge, Sheen told Wallace, "I'll just say this: It was epic. There are two rules at my house right now: You park your judgment at the door, and you enjoy every moment. People can interpret that however they want. Enjoy every sober moment. Enjoy every loaded moment. Just enjoy every moment. It's not a rehearsal, you know?"
>> The 22-year-old Jordan described a recent sexual encounter with Sheen: "He was, like, 'Will you blow me? Blow me while I do a hit,'" Jordan recalled. "So I did that," she added, noting that Sheen asked to be held afterward. "I think he was scared. I could see the pain."
>> Jordan also described the last time she saw Sheen. "As I was walking away, I could see him just sitting in bed, hunched over with his pipe," she said. "That night I knew: This is the most self-destructive person I have ever met."
>> Added Penn: "When you divorce the moral judgments, which I prefer to do, I see a guy who has a clearer view of the nature of the world around him than is sometimes comfortable to have. Those are the sort of people who have a tendency to find altered states. But he's a very ironic character. He's got pretension in the crosshairs of his wit. I think to a large degree he's saying, 'Guys, we're only going to be here once, so lighten the f— up.'"