Born in Kezmarok, Czechoslovakia, Radoslav Suchy starred with SKP Poprad before joining the Sherbrooke Faucons of the QMJHL in 1994-95. After parts of three seasons in Sherbrooke, Suchy helped the Chicoutimi Sagueneens reach the Memorial Cup in 1997 where he was named the most sportsmanlike player at the tournament and was QMJHL Second Team All-Star.

An offensive defenceman in junior, Suchy signed with the Phoenix Coyotes in September, 1997 as a free agent and was a solid regular in the AHL and IHL for two seasons. He played 60 games as an NHL rookie in 1999-00 and represented Slovakia at the 2000 World Championships. Suchy improved his overall game in 2001-02 while averaging over 17 minutes per game, becaming one of the Coyotes more reliable blueliners.

After making his World Championship debut in 2000, Suchy returned to the tournament in 2003 and again in 2005, while representing his homeland at the 2004 World Cup of Hockey. The former QMJHL star went on to play parts of seven seasons with the Coyotes oraganization before being acquired by the Columbus Blue Jackets in the summer of 2004.