Giffey committed to play basketball at the University of Connecticut under coach Jim Calhoun. As a freshman, he was a reserve on the squad which won the 2011 NCAA Men's Division I Basketball Tournament. After winning the tournament, he said, “It was such an emotional time for me, that this university, this team, became such a big part of my heart and became so close to me that it never crossed my mind to leave this place. I always felt it was about being a student-athlete at UConn. This school gave me so much when I won my national championship with this team.”[4] Giffey scored four points and grabbed six rebounds in the championship game against Butler. On the season, he averaged 2.2 points and 1.4 rebounds in 9.9 minutes per game.[3]
As a sophomore, Giffey averaged 2.6 points and 1.5 rebounds per game. He missed the first game of the season after hyperextending his elbow in the preseason.[3]
As a junior, he averaged 4.9 points and 3.6 rebounds per game.[3] He injured his knee in a game against Cincinnati on 3 March 2013 and missed the remainder of the season.[5]
Following graduation, Giffey played on the 2014 Memphis Grizzlies summer league team and then the Utah Jazz summer league team.[7] On 15 July 2014, the German team Alba Berlin announced that they had signed him for three seasons.[8]
On 29 July 2019, Giffey extended his contract with Alba for two more seasons, until 2022.[9] Serving as the Berlin team captain, Giffey won the German national championship[10] as well as the German Cup competition in 2020.[11] During the 2020–21 season, he averaged 8 points and 2.8 rebounds per game.
Giffey's first tournament with the senior Germany national team came at EuroBasket 2013, where he contributed with averages of 9.2 points and 3.2 rebounds per game.[19]
The next international tournament for Giffey with Germany, would occur six years later, at the 2019 FIBA World Cup, where he played a limited role during the competition.[20] At the 2020 Summer Olympics in Tokyo, Giffey finished the event averaging 7.3 points and 1.8 rebounds per game.[21]
In 2022, Giffey helped Germany earn a bronze medal finish at the EuroBasket, producing 5.9 points and 1.9 rebounds per game.[22] The following year, he was a member of Germany's 2023 FIBA World Cup title winning team, averaging 3.1 points per game during the event.[23]