Sabovčík was born on 4 December 1963 in Bratislava. His mother, Alexandra, was a ballerina of Czech descent, and his father, Jozef, a dancer and choreographer of Slovak descent. He is Catholic, speaks five languages, and has dual Slovak and Canadian citizenship. In 2005, he stated that he did not agree with the dissolution of Czechoslovakia and still felt Czechoslovak. His first marriage was to Canadian champion Tracey Wainman, with whom he has a son named Blade, and his second marriage is to Jennifer Verili, with whom he has a son named Jozef Junior. They live in Bountiful, Utah.
Career
Sabovčík began skating when he was six years old. His main coach was Agnesa Búřilová but he also worked with Anderlová, Lojkovičová, and Hilda Múdra. His choreographer was Frantisek Blazak. Sabovčík won bronze at the 1981 Skate Canada International and 1982 Skate America. He was the silver medalist at the 1983 European Championships. Sabovčík had knee effusion before the 1984 Winter Olympics in Sarajevo. He won the bronze medal behind Scott Hamilton and Brian Orser. Sabovčík became a two-time European champion with wins in 1985 and 1986. He also won 1985 Skate Canada International and Skate America. Sabovčík landed a quad toe loop at the 1986 European Championships. It was approved at the time as the first quad in competition but a few weeks later ruled invalid because of an alleged touchdown with his free foot. Despite a knee injury, he had to compete at the 1986 World Championships because his federation did not believe he was really injured. He said, "It was the hardest 4½ minutes of my skating career, knowing that I had to finish, but could hardly walk, let alone skate." Having undergone three knee operations, he retired from competition in 1986. Nicknamed "Jumping Joe", Sabovčík was known for his jumping ability and later turned it into a lucrative professional career. He is known for an excellent tuck Axel. "Sometimes there is beauty in simplicity and I think an open Axel is very beautiful. A tuck Axel is basically the same thing, but it has a little more edge to it, which is great for me, because I can use it with my rock numbers. If you noticed in my slower, quieter programs I always do an open Axel as it's better suited for that kind of music." He was disappointed by the loss of compulsory figures, saying, "In my opinion, the quality of skating itself has gone down. Figures taught how to use edges, like Robin Cousins and Brian Boitano still do, that with a couple of pushes they can get across the whole rink, you don't see that with the new skaters." Sabovčík coaches skating at the Bountiful Recreation Center in Utah.