Sheen - real name Carlos Irwin Estevez - was booked for investigation of second-degree assault, menacing and criminal mischief after allegedly fighting with Mueller during their festive celebrations in Aspen, Colorado, where they were spending the holidays with their nine-month-old twin sons.
He was released on Friday (25Dec09) on $8,500 (£5,315) bond and returned to Los Angeles, while Mueller remained in Aspen.
An affidavit obtained by GossipCop.com reveals the couple began arguing after Mueller said she wanted a divorce.
The police statement reads, "Mueller and Estevez were in an argument in the upstairs bedroom... Mueller told Estevez that she wanted a divorce, that Estevez then pulled out a knife, holding it to her throat, saying, 'You better be in fear. If you tell anybody, I'll kill you. Your mother's money means nothing - I have ex-police I can hire who know how to get the job done and they won't leave any trace.'"
In the same papers, Sheen denies "threatening Mueller with a knife or strangling her" but Aspen police officer Rick Magnuson, who filed the report, notes that Mueller "had red marks on the upper part of the front of her neck".
Magnuson also reports that Sheen showed him a knife with a four-inch blade, which was in a travel bag outside the bedroom the couple had argued in.
Sheen's menacing charge is the most serious and usually carries a sentence of two to eight years in prison and a fine of $2,000 (£1,250) to $500,000 (£312,500).
Meanwhile, the couple is set to undergo counselling together in the New Year (10), according to Sheen's manager Mark Burg, who adds they have no plans for divorce.
The actor wed Mueller in May 2008 following a messy divorce from his now ex-wife Denise Richards.