NEW YORK — Give Woody Harrelson a piece of yarn, and he’ll knit you a full-on, multicolored sweater. Here’s his take on playing crafty mentor Haymitch Abernathy sober, as opposed to falling-down drunk in the past two Hunger Games films.

“I wanted to give him a little more of a tortured expression: Jesus Christ, sobriety! Honestly, when I was first playing him — I will generally go over the top if allowed,” says Harrelson, who credits directorial restraint for his more muted performance in The Hunger Games: Mockingjay — Part 1 (opens today in select cities and Friday nationwide). “A guy who’s an alcoholic, a lot of times you have no idea they’re drunk.”

One heavy drinker of Harrelson’s acquaintance, “he was big on grapefruit and vodka, with very little grapefruit. He could carry the thing and never spill a drop. He was so functional. It was impressive. He has since passed. He was a good character.”

In a sense, Harrelson, 53, is the epitome of Haymitch, the shambling former games champion who hides a pointed intelligence and canniness under a cloak of cluelessness. But don’t be fooled by Harrelson’s at-times dopey grin, or apparent obtuseness, or his oft-referenced penchant for controlled substances — which came up last weekend in his Saturday Night Live opening dialogue, when he had trouble recalling 1989.(“The memories are a little fuzzy, because of the drugs,” he joked, ​referencing the past 25 years.)

Director Francis Lawrence says Harrelson kept him at arm’s length when he signed on for the second installment of the four-part film series, replacing Gary Ross. Lawrence (no relation to series star Jennifer Lawrence) called up each cast member to introduce himself and give them his take on the material.

“Woody took the longest time to connect with me,” says Lawrence. “His trust has to be earned. I had to fly to New York to see his play Furthest From the Sun and hang out at his apartment. It took a while.”

Their partnership bears dark, violent fruit in Mockingjay, with Harrelson’s Haymitch now clean, sober and bitter about leaving the booze in his past. He’s still mentoring freedom fighter Katniss Everdeen (Jennifer Lawrence) in her quest to overthrow the totalitarian regime of Panem.

Though Harrelson’s onscreen time in this movie isn’t hefty, “he’s very central,” the director says. “He’s betrayed Katniss and he has to make amends.”

And Harrelson himself understands Katniss’ unwillingness to live by rules that are meaningless to her.

“I’m an anarchist. You’ve got to defy certain unnecessary rules. But there are certain very good rules around traffic that are not adhered to in this town. I’m one of the idiots breaking them,” says Harrelson, who rode to this interview on his motorcycle, with his wife, Laura, sitting behind him. “For the important ones, I’m always on target. I had precious cargo in the back. That’s not even funny.”

Harrelson lives mostly in Hawaii with his wife and three daughters, staying largely out of the spotlight. So how does his rebelliousness manifest itself?

“I don’t believe in government. In other words, I think we can all look after ourselves. You want some mechanism that controls the traffic, absolutely. But generally, what the government accomplishes, 99% of that is (expletive),” he says. “I look at government as businessmen working for bigger businessmen. There’s obvious things — don’t steal, the Ten Commandments. There’s what we call victimless crimes. In my opinion, if you don’t actually have a victim who’s a human being, someone who’s been hurt or their property has been hurt, there’s no crime.”

Those are the values he instills in his brood: Deni, 21; Zoe, 18; and Makani, 8. His daughters don’t give him special treatment because he’s buddies with Lawrence, or one of the stars of one of the decade’s most lauded and profitable movie franchises.

“If that’s what made me a cool dad, I don’t know how much I’d respect them. It shouldn’t be any external factor that determines that,” he says. “But they do like it. They’re so immune to all this. They don’t live in L.A. They watch the movies, and they are great about it, but they don’t get caught up in things the way a lot of kids do.”