Haggans faced discipline after serving jail time in June after pleading guilty to DUI charges stemming from an April 2011 incident. His hearing before the NFL occurred on Sept. 5.
"We were certainly aware that this decision was a possibility as we evaluated Clark prior to adding him to our roster. Therefore, we are prepared to move forward accordingly," 49ers general manager Trent Balke said in a statement.
The 13-year-veteran was the 49ers' only backup at outside linebacker behind Aldon Smith and Ahmad Brooks, although he hasn't played a snap in his two games with the team. The 35-year-old was signed after 2011 starter Parys Haralson was placed on injured reserve with a torn left triceps.
"While we don't agree with the league's decision, we will abide by their ruling," Haggans' agent, Jeff Sperbeck, told the Bay Area News Group.
Smith, meanwhile, was the passenger in a car accident last Friday night in Santa Clara County when the driver swerved to avoid hitting a deer. He sustained a cut beneath his right eyebrow.
"I'm all right," he said. "I feel good. We walked away from it. I'm moving forward."
Smith played all the defensive snaps in Sunday night's victory over the Lions. He said it was good for him to be able to get on the field so quickly after the accident, in which the driver suffered a "broken back," according to the California Highway Patrol.
"Being in something like that -- being in an accident -- and then being able to go out and have fun and do something that I love doing -- it was a relief to be able to get away from everything," Smith told reporters. "So it was good that I was able to get out there and make plays and get the win. So I was fine."
Information from The Associated Press was used in this report.