As of the current data for Ash catching Mewtwo the answer is no. Right now nobody has captured Mewtwo due to the fact that he is such a strong pokemon.
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how do you catch a mewtwo on Pokemon platinum
No you can't catch Mewtwo in Pokemon silver, you must trade it from Pokemon yellow.
Catch 'em all
There is no such Pokemon as "Shadow" mewtwo. There is a regular mewtwo that you can catch like any other Pokemon. It's located in the Cerulean Caves.
you catch it in cerulean cave