The Guardians designated Gibaut for assignment Tuesday, Mandy Bell of MLB.com reports.
Gibaut was dropped from the 40-man roster so the Guardians could clear a spot for catcher Sandy Leon, who was acquired from the Reds on Tuesday and is set to serve as Cleveland's No. 2 backstop behind Luke Maile while Austin Hedges (concussion) is on the 7-day injured list. The 28-year-old right-handed reliever has spent the majority of the campaign at Triple-A Columbus, though he was called up from the minors Monday and pitched 1.1 innings out of the bullpen in Monday's 11-1 loss to the Twins.