Khamutowski started his career in 1994 with
Smena Minsk, a club from the Belarusian third division. Since 1995, he has been regularly transferring from one club to another and subsequently played for
Ataka-Aura Minsk in 1996,
BATE Borisov in 1998,
Smena-BATE Minsk in the same year, again BATE Borisov in 1999 and then again Smena-BATE Minsk, also in 1999. In 2000, he moved to
Torpedo-MAZ Minsk before transferring abroad for the first time in the summer of the same year, to German side
Waldhof Mannheim, who played in the
2. Bundesliga at the time. However, he spent the entire season with the German team as the second-choice keeper and only made two league appearances. He went on to move to Russian side
Dinamo Moskva in 2001, but soon moved to
Volgar GP Astrakhan for the beginning of the 2002 season. However, he only spent one half-season with the team before moving to
Metalist Kharkiv for the 2002–03 season. In the summer of 2003, he joined Romanian team
FCSB on a free transfer, signing a contract until January 2007. He played three seasons for FCSB and won the
Romanian league title twice. In early 2006, he left Romania and joined
FC Tom Tomsk, signing a two-year contract. In 2012, he said that "The main problem of the Russians is an undeveloped infrastructure. When people come to old, gray, dilapidated stadiums, and water pours on top of them – how to drive wives and children there? This is especially characteristic of the Urals and Siberia. But clubs have solid budgets; in principle, they could quietly develop in this regard. But where finance wasted, I do not know. It's good that the situation is changing now. We would have to tighten up management, because in Russia this is a problem." In January 2008, he joined
FC Carl Zeiss Jena, a relegation-threatened side in the German Second Bundesliga, where he signed a contract until the end of the season with an automatic one-year extension in case the club managed to stay in the Second Bundesliga. He helped the team reach the semi-finals of the
German Cup, where they were knocked out by
Borussia Dortmund. Following Carl Zeiss Jena's relegation to the
3. Liga, he signed a two-year contract with
FC Augsburg, where he injured his shoulder. He was released on 30 June 2010. In March 2012, he came back to Romania, signing a contract for three months with
Petrolul Ploiești. On 1 June 2013, he won the
Cupa României 1–0 against
CFR Cluj, playing in the
final. ==International career==