In a new interview with PEOPLE, Grammer spoke about the murder of his late sister, Karen, and how he turned to drugs and alcohol to cope with her tragic death — something he details in his new book, Karen: A Brother Remembers.

Karen was just 18 in 1975 when she was kidnapped, raped and brutally murdered in Colorado Springs. And while her killer, Freddie Glenn, was later convicted, the damage it did to Grammer and their family was permanent.

In the wake of Karen’s passing, Grammer struggled with substances, and between 1988 and 1996, he faced multiple arrests for DUI and cocaine possession, and even checked into the Betty Ford Center.

“I always had something in the back of my head saying, ‘Okay. That’s enough now. Cut it out. You know why you’re doing this,'” he told the outlet. “But there was the other part of me that wanted to surrender to it and go, ‘Let it mess you up a little bit. Let it hurt.'”

It’s something he touched on in a separate interview on Good Morning America, adding that it’s “remarkable” he survived during the period in his life, telling Diane Sawyer, he was often drunk or high while working.

Even at his lowest, Grammer showed up to set, playing Dr. Frasier Crane, first on Cheers from 1984 to 1993 and later Frasier, which ran from 1993 to 2004.

“It seemed to make it more damning in a way, but you know what? I had to do it, so I’m okay,” Grammer told PEOPLE. “I learned that I really am a ‘I don’t quit’ kind of guy. I can look at the past and see, ‘Oh, well, you still did what you had to do.'”

The memoir dives into the dark details of Karen’s murder, but also celebrates the vibrant life she lived — something Grammer says the world never really got to see.

Painting a picture of Karen as a free-spirited and loving woman who made the most of every moment, Grammer said for a long time after her death, the grief was so all-consuming that he “couldn’t access happiness.”

“The book helped me get to a new place with that,” he told the outlet. “I wanted to breathe life into her, to welcome her into the world again.”

Karen isn’t the only tragic loss in the actor and his family had faced. His father, Allen Grammer, was murdered in 1968. Just five years after Karen’s death, his half-brothers, Billy and Stephen, died in a suspected shark attack in the Virgin Islands.

“There’s a legacy of early death in my family,” Grammer said. “I pray to break that cycle.”

Elsewhere in the book, Grammer returns to Colorado Springs, where he retraced his sister’s last steps

“She had fallen backward from the trailer door after knocking for help,” he said of her final moments after the attack. “She had been on her knees, crawling her way. Seeking help with her last ounce of life.”

“The coroner noted that through a gaping wound in her neck, he could see all the way into Karen’s lung,” he wrote in the book. “I had been right in saying he almost decapitated her. Freddie Glenn punched holes in my sister’s body with unimaginable brutality. There were defensive wounds on her hands.”

Returning to Colorado Springs, however, helped him finally gain some closure on her death. — though it’s a word he says he hates.

“I had to complete my farewell to her,” he noted. “I hate the word ‘closure,’ but I finally got to say all the things I never said.”

“The mission is to heal, but the mission is also to help other people,” Grammer added in his conversation with GMA. “And by introducing them to Karen, it is my hope that they’re re-introducing themselves to the loved ones they lost, in the same way.”

Karen: A Brother Remembers hits shelves May 6 and is available for preorder now.