There is nothing in this planet that can eliminate criminal activity.

Blockchain can minimize illegal activities as there are a lot of middlemen who will not be required, once blockchain in implemented. When less people are involved, obviously less illegal activities will take place.

Elimination of criminal activities is not possible at all as most of the domestic crimes are driven by ego or emotional issues. If Murder takes place because of jealousy, betrayal, competition etc, blockchain can't help to stop that.

It won't be able to eliminate human bad emotions and hence it will not be able to totally eliminate criminal activities. However a lot a illegal activities can be curbed.