This is a great question! The seafloor is destroyed in places called subduction zones, where one tectonic plate sinks below another tectonic plate. The seafloor is mostly made of a rock called basalt. As the seafloor sinks in the subduction zone, the basalt goes through a process called "metamorphism"; the heat and the pressure that the seafloor experiences causes the basalt to transform first into a rock called blueschist and then into a rock called eclogite. Eclogite is composed mostly of two minerals that are called garnet and omphacite. Eclogite is very, very heavy, so once the seafloor transforms into eclogite, it can sink all the way to the boundary between Earth's core (the innermost layer) and the mantle (the layer below the crust, which is the part of Earth we walk around on everyday). Once the seafloor sinks all the way to the core-mantle boundary, it gets recycled and becomes part of the mantle, where eventually it may remelt and form new seafloor.

It depends on what you mean by destroying seafloor. If you mean what happens when ocean crust is subducted, which is to say, when a slab of seafloor at the edge of a tectonic plate is pushed under another plate so that the ocean crust goes down into the mantle, what is left behind is more seafloor. New ocean crust is created on the other end of the plate, so the whole seafloor moves like a giant, very slow (moving at a few centimeters per year) conveyor belt. If you mean what happens when seafloor is damaged by activities such as mining, then what is left behind is torn up seafloor with fewer microbes and fewer animals like worms and sea cucumbers. Some areas may also be covered with the sediment that was dug up and dumped back, though this seems to spread out. Changes in seafloor environments generally occur very slowly, so they can take a very long time to recover from disruptions.