2006-07: David Wolf appeared in one men's game with Heibronner Falken as a 17-year-old; skating for the Jungadler Mannheim U18 team in Germany and playing in one game for Germany at the 2007 U18 Division 1B World Junior Championship. He had no points nor penalty minutes with either the Falken or Germany's U18 team. In 27 regular season games for Jungadler he scored 14 goals with 22 assists and 93 penalty minutes. Mannheim was first in Germany's U18 league in the regular season but lost to second-place Kolner EC in the playoff finals. Wolf scored 2 goals with 1 assist and had 40 penalty minutes in five playoff games.
2007-08: Wolf skated for Eispiraten Crimmitschau in Germany's second men's division. In 46 regular season games he scored 7 goals with 2 assists and 40 penalty minutes. Crimmitschau finished eighth in the 16-team second division. Wolf had 1 assist and 6 penalty minutes in six playoff games.
2008-09: Wolf led last place Crimmitschau with 120 penalty minutes and scored 2 goals with 6 assists in 36 games in his second season with Eispiraten. He played for Germany's U20 team in the 2009 World Junior Championship. Wolf scored 1 goal and was -3 with 53 penalty minutes as Germany finished 9th out of ten teams in the 2009 WJC.
2009-10: Wolf moved up to Germany's DEL as a 20-year-old — skating for the Hannover Scorpions — and played in seven games for the Fischtown Pinguins in the German second league. He scored 4 goals with 7 assists and was minus-4 with 40 penalty minutes in 54 regular season games with the Scorpions. Hannover was fourth in the regular season before capturing the playoff championship. Wolf scored 3 goals and was +2 with 12 penalty minutes in 11 playoff games. He scored 2 goals with 2 assists and had 33 penalty minutes with Fischtown.
2010-11: Wolf played in 55 games for Hannover — including four playoff games with the Scorpions — in his second DEL season. He scored 2 goals with 4 assists and was minus-5; leading Hannover with 97 penalty minutes in the regular season. Hannover finished fifth and reached the second round in the playoffs. Wolf scored 1 goal with 1 assist and had an even plus/minus with 52 penalty minutes in the playoffs. In one second division game with the Hannover Indians he had 3 assists and 4 penalty minutes. In March 2011 he signed a contract to play for the Hamburg Freezers in 2011-12.
2011-12: Wolf had a career-high 35 points while leading the DEL in penalty minutes in his first season with Hamburg. He scored 12 goals with 23 assists and was +14 with 167 penalty minutes in 46 regular season games. The Freezers were fifth in the regular season and reached the second round in the playoffs. Wolf was minus-2 with no points and 2 penalty minutes in five playoff games.
2012-13: Wolf was Hamburg's second-leading scorer behind one-time Maple Leafs' prospect Jerome Flaake and skated for Germany's national team in three qualifying games for the 2014 Winter Olympic Games. In 49 regular season games he scored 17 goals with 19 assists and had 96 penalty minutes and was +11 as Hamburg finished fifth in the DEL. The Freezers reached the second round in the playoffs and Wolf scored 1 goal with 3 assists, finishing +2 with 26 penalty minutes, in six playoff games. He scored 2 goals with 1 assist and no penalty minutes in three games for Team Germany.
2013-14: Wolf once again finished second to Flaake in scoring for Hamburg while leading the club in penalty minutes in his fifth DEL season. He scored 14 goals with 26 assists and was +14 with 152 penalty minutes in 48 regular season games. The Freezers finished first in the DEL in the regular season but after defeating Iserlohn in the quarterfinals lost to ERC Ingolstadt in six games in a best-of-seven semifinal series. Wolf scored 4 goals with 8 assists and was +4 with 47 penalty minutes in ten playoff games. He signed a one-year entry-level contract with the Calgary Flames in May 2014.
Wolf signed an NHL contract with the Calgary Flames on May 12th, 2014.