It's promoted as part of the Blue economy.

From MIT

Deep Sea mining, like asteroid mining, is a relatively unconventional method of extracting Rare Earth elements (REEs). Unlike asteroid mining, however, deep sea mining has already been undertaken through projects such as deep sea diamond mining. Actual mining for REEs has not been attempted because of environmental issues and cost. These issues are much more complicated and not as easily fixed as other concerns. Deep Sea mining would be an effective way to obtain a large amount of rare earths; in one specific section of the ocean floor, "...one square kilometer could meet a fifth of the world's annual consumption of rare metals and yttrium..." (Phys.org, 2011). However, the economic viability of deep sea mining is still questionable. If the environmental and financial factors were cleared, then deep sea mining would definitely be a feasible option for the long term.

The environmental factors are not cleared but that didn't stop governments from issuing permits.
From Deep Sea Mining Campaign

“It is disappointing that so many exploration licences have been issued without any understanding of the environmental impacts of exploration, let alone exploitation. It also facilitates the development of an industry that does not have the consent of potentially affected communities and wider civil society. This industry has not gained a social licence to operate,” says Dr. Rosenbaum.

Dr. Catherine Coumans of Mining Watch Canada, said, “As the global steward of the world’s oceans it is incumbent upon the ISA to protect the world’s already stressed marine ecosystems. The deep sea is one of world’s last ecosystems to have largely escaped devastating impacts of mining, and as an ecosystem that affects all life on earth it must be protected.”

Deep Sea Mining – A new frontier for ecosystem destruction

Once again, a Canadian mining company is leading the way in pioneering a highly dubious mining practice. And again the country of choice for this latest environmental experiment is Papua New Guinea (PNG). Canada’s Barrick Gold is using the 800 kilometre-long Strickland River system in PNG as a dumping ground for its unconfined mine waste (a practice that is not permitted in Canada), and Canada’s Placer Dome used the sea as a dumping site for its mine tailings by piping them into the ocean from its Misima Island mine (also not permitted in Canada). Perhaps for the industry it is a short step from dumping unconfined mine waste into the ocean, to actually mining the ocean floor. This is what Canada’s Nautilus Minerals Inc. (Nautilus) plans to do in the Bismarck Sea, some thirty kilometres off the coast of PNG between the islands of New Ireland and New Britain.
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Very little is known about the deep sea environment - it is often commented that more humans have walked on the moon than have visited the sea at these great depths[5] and that we have more detailed maps of Mars than we have of the deep sea. Why then are mining companies such as Nautilus granted the opportunity to mine and destroy what has not yet been fully explored, with undetermined consequences for the marine environment, for associated terrestrial communities and natural systems, for human knowledge about the origins of life on earth and about potentially beneficial genetic resources? Part of the answer lies in the fact that within the territorial waters of a nation, where the Nautilus project is located, that country can issue permits for exploration and exploitation at will.

My guess is that Global Deep Sea Mining may be one of the incentives for pushing the TPP. The regulations come from the UN Conventions on the Law of the Sea, dated 1982 with many countries refusing to sign.

Upsetting parts of the world essential to the absorption of carbon dioxide? This is all we need right now!
Scientists, environmentalists call for freeze in deep sea mining permits

In a paper published Friday in Science, the experts ask the International Seabed Authority (ISA), which is the arm of the United Nations Convention on the Law of the Sea that governs mining in international waters, to first come up with environmental regulations on the emerging industry.

Environmentalists have attacked this and other projects. They argue that mining should be prohibited globally, but in specific areas of the ocean floor, as the activity could upset parts of the world that are essential to the absorption of carbon dioxide, causing long-term damages to the environment.

"These ecosystems do not recover — they just don't," Jack Kittinger, one of the paper’s authors and director of Virginia-based Conservation International told The Washington Post. "We're talking geologic time here because it's so deep and so cold."