Unfortunately, the DMCA doesn't allow to submit a removal notice for a whole website. Removal notices can only be submitted for specific webpages. If you want to remove all the infringements hosted by a website, you need to submit a notice (a "Blast" in the case of Blasty) for each and every infringing webpage of the website.
That's exactly what Blasty Full Power does. It crawls the web and each time it finds an infringing webpage, it submits a DMCA copyright removal notice to Google, Bing, Yahoo and the host of that infringing webpage.
Google's DMCA demotion signal for web search
Receiving Blasts has damageable consequences for a domain. Google has implemented a demotion signal for domains which receive large numbers of DMCA notices. Meaning that the more Blasts your submit for a website, the more Google's search ranking algorithms will demote that website.