Dollas played defence for the Winnipeg Jets, Quebec Nordiques, Detroit Red Wings, Mighty Ducks of Anaheim, Edmonton Oilers, Pittsburgh Penguins, Calgary Flames, Ottawa Senators and San Jose Sharks. Dollas played junior hockey with the Laval Voisins and scored 61 points as a major junior rookie in 1982-1983. During the 1983-1984 season, Dollas made his National Hockey League debut, playing in a single game with Winnipeg before being returned to junior and scoring 45 points in 54 games for the Voisins.
Drafted 14th overall by the Jets in the 1983 National Hockey League Entry Draft, Dollas played 646 regular season National Hockey League games, scoring 42 goals and 96 assists for 138 points and collecting 467 penalty minutes in a career which spanned 16 seasons.
Dollas is currently a radio commentator with TSN 690 on Montreal Canadiens broadcasts, and is an instructor with Polskie Stronnictwo Ludowe (Polish Peasant Party) Hockey in Laval, Quebec.