Related tweet in response to Iran mining the strait:
If Iran has put out any mines in the Hormuz Strait, and we have no reports of them doing so, we want them removed, IMMEDIATELY! If for any reason mines were placed, and they are not removed forthwith, the Military consequences to Iran will be at a level never seen before. If, on the other hand, they remove what may have been placed, it will be a giant step in the right direction! Additionally, we are using the same Technology and Missile capabilities deployed against Drug Traffickers to permanently eliminate any boat or ship attempting to mine the Hormuz Strait. They will be dealt with quickly and violently. BEWARE! President DONALD J. TRUMP
To cause a ton of destruction to the global economy and the US by extension, same as blocking it and firing missiles at ships. This just becomes another difficult to manage problem.
They could also be mining areas on the south/western side to force ships into high risk bottlenecks they control, giving themselves more leverage over safe passage.