Moscow dealt severely with the breakaway republic of chechnya in the 1990s and 2000s because

They did it because the country had a tradition of being a part of Russia that lasted for over 500 years.

Chechnya was an important part of Russian history and has been a part of the Russian state for over 500 years. When the problems began, Russians believed that it was illegal to breakaway and they wanted to protect the territorial integrity of the Russian country. This is why the war began and we all know how it ended.