Officers arrested Mitchell Taylor in Redmond and booked him into King County Jail. He appeared in King County Superior Court on Friday afternoon and was ordered held on $600,000 bail.
Murray's staff noticed the comments Tuesday on the mayor's Facebook page, according to police reports.
They included explicitly homophobic, racist and misogynistic comments, the milder of which included, "Mayor return to hell where you came from," "death to socialist council member," "Death to Seattle police" and "feminist must get raped and die," court documents show.
Councilwoman Sawant, elected in November 2013, is Seattle's only self-proclaimed socialist councilmember.
The comments also made references to Harvey Milk, San Francisco's first openly gay elected official, who was assassinated in 1978.
Murray is Seattle's first openly gay mayor.
The comments were made under the defendant's real name.
Detectives on Thursday showed the comments to Murray and Sawant. Both said they interpreted the comments as threats to their lives.