The team also outrighted left-hander Michael Kirkman to Round Rock after he cleared waivers Tuesday.
McCutchen, who will be the long reliever, signed a minor league contract in December and was added to major league camp last week. He has a career 4.77 ERA in 108 games, including 15 starts, with Pittsburgh from 2009-12.
Gimenez joined Texas on a waiver claim from Oakland on Friday. He was on the opening day roster but didn't play in a 14-10 loss to Philadelphia. The Rangers have 10 days to trade, release or outright Gimenez to the minors.
Kirkman was designated for assignment when the club claimed Gimenez.