Did they really collaborate with the Nazis? It's baffling to me that the USSR would do it in such a brutal way and just after the war ended.
Correction - it was done during the war, in May 1944.
Soviet reasoning was the same as in case of deportations of Chechens and Ingushs (in January 1944) - collaboration with the enemy. And there're plenty of such episodes, which doesn't really justifies fact of deportation or practice of collective punishment in general.
It's somewhat similar with deportation of Soviet citizens of German ethnicity (August 1941).
The Red Army was unexpectedly ineffective during the battles for the peninsula, and this had nothing to do with Crimean Tatars, only with the incompetence of the Soviet generals. So Stalin probably decided to mask these facts by laying all the blame on the local non-Russians. My source: http://ru.krymr.com/a/27851629.html (it's in Russian, sorry)