Born in Cherkasy, Ukraine, Mykhailiuk's mother is Inna, a high school biology teacher, and his father is Yuriy, a college history professor. He attended high school at Cherkasy First City Gymnasia.
Mykhailiuk played for the Under 20 Ukrainian national team in the 2016 FIBA Europe Under-20 Championship in Helsinki. During the tournament Mykhailiuk led his team in scoring at 14.9 points per game in seven tourney games. He hit 36.8% of his floor shots. Mykhailiuk shot 47.2% from two and 19% from three point territory. He made 85.7% of his free throws and also grabbed 5.6 rebounds a game with 2.7 assists and 4.7 turnovers with 2.1 steals per game.
Mykhailiuk played for the Ukrainian national team, which competed at the 2014 FIBA Basketball World Cup, in Spain August 30 to September 14.
In the summer of 2013 he played with the Ukrainian national team in the 2013 FIBA Europe Under-16 Championship. He was selected in the All-Tournament Team, after completing an outstanding championship, averaging 25.2 points, 8.0 rebounds and 3.4 assists per game.
Mykhailiuk received offers from Virginia, Iowa State, Oregon, and Kansas. On May 21, 2014, Mykhailiuk committed to play basketball at the University of Kansas and played for the team during their 2014–2015 season. During his freshman season, he started five of the first seven games of the season, averaging 21.3 minutes a game, but his playing time since then was significantly curtailed. He scored 11 points while playing 32 minutes in the Orlando Classic Championship game against Michigan State on November 30, 2014. He was the youngest player in Big 12 Conference history at 17 years old.
Returning to Kansas in his sophomore year Mykhailiuk has averaged 5.4 points, 1.3 rebounds, and 0.9 assist per game in 35 games of the 2015-2016 basketball season, while hitting 40.2% of his three point shots. On November 23, 2015, Mykhailiuk scored 18 points against Chaminade University. In the first round of the 2016 NCAA basketball tourney, on March 17, 2016, Mykhailiuk scored 23 points, setting his personal college career scoring record, with 9 of 11 field goals and 4 of 5 threes against the Austin Peay Governors.
Mykhailiuk returned to the Kansas Jayhawks for his junior year in college. On December 22, 2016, in game against UNLV Mykhailiuk scored 20 points with 6 rebounds, 2 assists, and 2 steals, assisting KU in a 71 to 53 win in Las Vegas. In the UNLV game, Mykhailiuk made 4 of 6 three point attempts. In the 2016-2017 season, Mykhailiuk has averaged 10.6 points a game, 3.5 rebounds a game, and 1.6 assists per game, while shooting 41.5% from three point territory. On April 12, 2017, Mykhailiuk decided to enter the 2017 NBA Draft, but did not hire an agent. This will allow him to return if he decides by May 24.