In his first week in the league, he had a 3-block game against the Los Angeles Clippers. On December 8 in his first game against Utah and former teammate and fellow Big Ten Player of the Year Burke, Stauskas posted career highs of 15 points and 8 rebounds. Stauskas again posted 15 points against the New York Knicks and former Michigan teammate Hardaway on March 3. On March 24, he received the nickname "Sauce Castillo" via social media after a closed captioning error. Stauskas started in the Kings' April 15 season finale against the Los Angeles Lakers and tallied 5 assists. It was his first and only start of the season. On July 10, 2015, Stauskas was traded to the Philadelphia 76ers along with Carl Landry, Jason Thompson, a future first round pick, and the rights to swap first round picks in 2016 and 2017, in exchange for the rights to Artūras Gudaitis and Luka Mitrović. During the preseason, Stauskas was impaired by a right tibia stress reaction. Although he felt recovered from the stress reaction by the beginning of the season, he missed the October 28 season opener with back spasms. The 2015–16 76ers team played no players over the age of 24 or with more than 3 years of NBA experience on opening night. Stauskas joined the young team's rotation in October 30 against the Utah Jazz with a 12-point debut performance. Stauskas moved into the starting lineup on November 2 against the Cleveland Cavaliers. He posted a career-high tying 15 points against his idol LeBron James. On November 7, Stauskas posted a career-high 18 points and career-high tying five assists against the Orlando Magic. He tallied at least 12 points in each of his first five games of action for Philadelphia. However, by mid November, Stauskas was deep in a shooting slump. He was scoreless in back-to-back starts, going 0-for-10 (0–5 3-point shots) combined against the San Antonio Spurs and Dallas Mavericks on November 14 and 16. Fortunately for Stauskas, his backup, Isaiah Canaan, was in a simultaneous slump, going 3-for-20 in the same games. However, Stauskas had a left knee contusion on November 23 against the Minnesota Timberwolves and was sidelined for the second half and the subsequent three-game road trip. He missed only one game and returned to the lineup on November 27 in limited minutes off the bench.