After a childhood in karting, Saavedra drove in Formula BMW USA for Gelles Racing, finishing 11th in points.

[1] In 2007 he switched teams in Formula BMW USA to Eurointernational and captured one win and finished 12th in points despite only competing in 8 of 14 races.

In 2009 he signed to drive in the American Firestone Indy Lights Series in 2009 for defending championship team AGR-AFS Racing alongside teammate J. R. Hildebrand.

He captured his first Indy Lights win in the fourth race of the season and the first on an oval, at Kansas Speedway in April.

While he was in the hospital being checked out, and with no working car to attempt to re-qualify, Saavedra appeared out of the race when Tony Kanaan bettered his time knocking him out of the field.

The following month, Saavedra captured Bryan Herta Autosport's second Indy Lights win in the AvoidTheStork.com 100 at Iowa Speedway.

Saavedra competed in the IndyCar Series season finale at Homestead Miami Speedway for Conquest Racing.

He was replaced in the Conquest car by João Paulo de Oliveira for the Motegi race and Dillon Battistini at the Kentucky Speedway, but returned to the car for the season finale in Las Vegas, which was cancelled after Dan Wheldon's fatal crash.

[7] In 2019, Saavedra participated on International Motor Sports Association (IMSA) 24 Hours of Daytona race, winning the LMP2 class in the #18 DragonSpeed Oreca 07, piloted by Pastor Maldonado, Roberto Gonzalez, Ryan Cullen and himself, overcoming an engine problem which nearly jeopardized his race.