They also called on Ms Cheney, the third highest ranked Republican in the House and one of just 10 from the party to back impeachment, to “immediately” resign and promised to withhold future political funding.
Wyoming Republican officials said the vote represented widespread anger at the congresswoman.
“No county in the state has heard this resolution and ultimately voted it down,” Carbon County Republican Party Chairman Joey Correnti IV told the Casper Star Tribune.“Seventy percent of the counties in this state took it up, and every single one passed it. That is the voice of the people.”
Ms Cheney stood by her decision.
“My vote to impeach was compelled by the oath I swore to the Constitution,” Ms Cheney told CNN on Saturday following the vote. “Wyoming citizens know that this oath does not bend or yield to politics or partisanship.”
Ms Cheney still has the backing of her House colleagues though, who voted 145 to 61 to keep her on as conference chair on Wednesday.
The vote wraps up a week that’s seen an extraordinary amount of division within the Republican party, which operated as a mostly united front during the Trump years, and banded together to resist the Obama administration at nearly every turn.
The day before the Wyoming censure vote, Democrats as well as a few Republicans voted to oust hard-right congresswoman Marjorie Taylor Greene from her committee placements, following revelations she previously endorsed conspiracy theories like QAnon, threatened her Muslim colleagues, and liked posts on social media calling for violence and death towards elected Democrats.
The tension over the future of the party has gotten so bad that one former Republican congressman, Charlie Dent of Pennsylvania, says he and others have begun discussing whether they should form a “new party or a new faction” after the “ugly populism” of the Trump years.