My Amphibious transporters storing only into shipyard or if they have an area where they can put dirt or stone or something else from excavator.

They can get anything from warehouses, but not put it in.

I'm not sure I understand your problem. It sounds like you have a mining tower with amphibious trucks assigned, and they're shipping direct to the Shipyard instead of to assigned storages for export?

No: On mining tower working, the trucks shipping nowhere, except dumping designations.

If this trucks not assigned to mining tower, they will work like other trucks (montage, demontage), but delivers goods from demontage not towarehouse, instead only to shipyard.

I've found it:

I don't recall ever setting it up that way. It must be a default setting that amphibious trucks aren't allowed to make warehouse deliveries.

Ahh! So it is like I first thought, and an occurrence of a bug I reported a while ago. You'll notice that trucks assigned to storages can also engage in prohibited deconstruction, even when they have other assigned work to do (see the bug thread), though I've recently noticed a reduction in that behavior so I think they're working on it.