Ortiz (4-4, 5.14 ERA) began the year in the Twins' rotation and won his first three starts, but was moved to the bullpen after going 0-4 with an 8.14 ERA in his next seven starts. He has made 18 relief appearances.
"Something happens, it happens," Ortiz said after his final game in a Twins' uniform, at Seattle on Wednesday. "We go over there, and we do the best we can over there. That is a very good team over there.
"[I was] not surprised because I don't pitch a lot."
The Rockies sent Triple-A infielder Matt Macri to the Twins in return. The Rockies will be paying what's left of Ortiz's $3.1 million contract this season.
Ortiz has returned to the Twin Cities to take care of some matters and is not expected to join the Rockies until Friday at Dodger Stadium.
The Rockies haven't announced a starter for Saturday on the road against the Dodgers, but manager Clint Hurdle said it will not be Ortiz. He has not started a game since May 26.
In addition, the Rockies were to place right-hander Aaron Cook (8-7, 4.12) on the disabled list after Wednesday night's game because of an oblique (side) muscle strain. He was originally slated to start Thursday against the Padres.
The club will call up righty Elmer Dessens from Triple-A Colorado Springs to take Cook's start. Dessens made 12 appearances for the Brewers (1-1, 6.60 ERA) before being designated for assignment on Aug. 4, when Milwaukee acquired reliever Scott Linebrink from the Padres.
The Rockies have lost righty Rodrigo Lopez (5-4, 4.42) for the season because of elbow surgery, and righty Jason Hirsh (5-7, 4.81) is iffy at best to return this season because of a fractured fibula. One of the possible reinforcements, right-hander Greg Reynolds, the No. 1 Draft pick last summer, was shut down at Double-A Tulsa because of shoulder pain.
The Rockies entered Wednesday's play five games behind the National League West-leading Diamondbacks and three games behind the Padres in the NL Wild Card race.
"It's been challenging," Hurdle said before Wednesday night's game with the Padres. "But we've worked too hard to get where we're at to not embrace it. We've got some people that are going to get opportunities, and we feel confident that they can do things."
The Rockies also recalled right-handed reliever Ramon Ramirez from Colorado Springs to fill the roster spot of center fielder Willy Taveras, who was placed on the 15-day DL on Wednesday because of a right quadriceps strain.
Taveras, who left Wednesday's game after 3 1/2 innings, has a .311 batting average and a team-high 29 stolen bases. Ramirez is 2-2 with an 8.82 ERA in 21 relief appearances in two previous stints with the big club.