Upshaw played high school basketball for San Joaquin Memorial High School in his hometown of Fresno, California. A top 100 recruit, he originally committed to play college basketball for Kansas State University, but was released from his commitment when Wildcats head coach Frank Martin left for another job. He then chose local Fresno State, where as a freshman in the 2012–13 season he averaged 4.1 points, 3.8 rebounds and 1.8 blocks per game. In the summer after his freshman season, Upshaw was dismissed from the Bulldogs for violations of team rules. The 7'0" center then transferred to Washington. After sitting out the 2013–14 season per NCAA transfer rules, he played 19 games for the Huskies, averaging 10.9 points, 8.2 rebounds and 4.5 blocks per game. On January 26, 2015, Upshaw was dismissed from the Washington program, again for violations of team rules. He was leading the country in blocked shots per game at the time of his dismissal and had led the Huskies in rebounding.
Upshaw declared his eligibility for the 2015 NBA draft rather than transfer to another college program. At the NBA Draft combine, Upshaw measured as one of the tallest players in attendance with the longest standing reach and wingspan. He was projected as a late first-round or early second-round selection, but went undrafted, likely due to his personal issues. In July 2015, he joined the Los Angeles Lakers for the 2015 NBA Summer League, where he averaged a mere 1.4 points and 2.2 rebounds per game. Upshaw felt there was more in him than his Summer League showing, and after dropping 20 pounds, he signed with the Lakers for training camp on September 14, 2015. He was later waived by the Lakers on October 20 after appearing in four preseason games. On October 31, 2015, he was acquired by the Los Angeles D-Fenders of the NBA Development League as an affiliate player of the Lakers. Upshaw received consistent minutes for the D-Fenders throughout the season before losing his spot in the rotation in late February 2016. On March 11, 2016, his contract was terminated by the D-League for violating the league's anti-drug program. In 28 games for the D-Fenders in 2015–16, he averaged 7.3 points, 4.5 rebounds and 1.4 blocks in 15.6 minutes per game.
On September 1, 2016, Upshaw signed with BC Kalev/Cramo of the Estonian League. He appeared in five games for Kalev/Cramo during October before leaving the team in November due to a knee injury.
After leaving Kalev/Cramo, Upshaw joined Mayrouba Club of the Lebanese Basketball League in late November 2016. He made his debut for Mayrouba in their 2016–17 season opener on December 2. In 18 games for Mayrouba, he averaged 19.7 points, 12.3 rebounds, 1.3 assists 3.6 blocks per game. In April 2017, he joined Iranian team Chemidor Tehran for a three-game stint.
On October 4, 2017, Upshaw signed with Champville of the Lebanese Basketball League. He left the team in February 2018. In 17 games, he averaged 13.4 points, 7.8 rebounds, 1.1 assists and 1.9 blocks per game.
In March 2018, Upshaw joined the Yakima SunKings of the North American Premier Basketball. He helped the SunKings win the championship. In five games, he averaged 11.2 points, 7.8 rebounds, 1.0 assists and 3.0 blocks per game.
