Astudillo signed his first professional baseball contract with the Philadelphia Phillies as an amateur free agent on December 15, 2008. In 2009, Astudillo played for the VSL Phillies. Midway through 2012, he was assigned to the GCL Phillies, and spent the 2013 season with the team as well. In 2014, he played for the Lakewood BlueClaws. In 2015, he was assigned to the Clearwater Threshers, where he would spend the season. On November 6, 2015, he elected free agency.

Known for an extremely high contact rate, Astudillo produced eight of the 30 lowest strikeout rates with a minimum of 100 plate appearances according to Baseball Prospectus’ catalog of over 42,000 individual seasons from 2005–2018. He produced the lowest of all at 0.9% in Venezuela in 2011, second-lowest at 1.8% in Venezuela in 2010, and fourth-lowest at 2.4% in the Florida State League in 2015.

On November 19, 2015, Astudillo signed a minor league deal with the Atlanta Braves. He spent the year with the minor league affiliate Mississippi Braves. He elected free agency on November 7, 2016.

On April 4, 2017, Astudillo signed a minor league deal with the Arizona Diamondbacks, and was assigned to the Reno Aces. He spent the year with the Aces and elected free agency on November 6, 2017.

On November 30, 2017, Astudillo signed a minor league deal with the Minnesota Twins and was assigned to the Rochester Red Wings. Astudillo was called up to the majors for the first time on June 29, 2018. He made his major league debut at Wrigley Field the following afternoon versus the Chicago Cubs as a defensive replacement in left field in the fifth inning, later switching to center field. In the sixth inning, he singled on a ground ball to second base to score Robbie Grossman for his first major league hit. On July 14, 2018, he made his major league pitching debut, completing the final inning of a 19–6 loss to the Tampa Bay Rays at Target Field. He allowed five runs on five hits and two home runs for a 45.00 earned run average (ERA) in his lone pitching entry of the season. Astudillo spent most of his playing time at catcher and third base and made other appearances at second base. He appeared in 30 games total for the Twins in 2018, batting .355, .371 on-base percentage, .516 slugging percentage, three home runs, 21 RBI, two walks and three strikeouts over 93 plate appearances.

The Twins announced their selection of Astudillo for his first major league 25-man Opening Day roster on March 27, 2019, as one of five bench players. One month later, he was placed on the injured list with a left hamstring strain. He was batting .327 with two home runs. He ended the season hitting .268 in 58 games.

On July 3, 2020, it was announced that Astudillo had tested positive for COVID-19.