It is a research vehicle that can report what the depth shows, but, it is not a workhorse.

The Mir I and Mir II (click here) are battery-powered, three-person submersibles with a maximum operating depth of 6,000 m (20,000 ft). This deep-diving capability ranks the Mir vehicles among the deepest diving submersibles ever built, and gives them the capability to reach approximately 98% of the ocean floor.

Who was the ocean explorer that raised articles from the Titanic? I am not sure what depth that was either.

The wreck of the RMS Titanic is located about 370 miles (600 km) south-southeast of the coast of Newfoundland, lying at a depth of about 12,500 feet (3,800 m).

Woods Hole did all the study of Titanic. (click here) Due to their study further was possible. 

James Cameron would know who had the equipment to work at the depths where the cargo ship sank. 

He knows the community. He has been doing incredible work 'at depth.' He'd be the man to talk to. 

The USA Coast Guard is responsible for finding survivors. The shipping company is responsible for it's ship, it's crew and it's cargo.