Did this recently so the memory is 'fresh' but not pleasant.
I had a clog between the bowl and the tank: I cut the barb end off of a hose and used it to ram the clog into the tank. It was really obvious when the clog cleared.
Later, when I tried to drain the tank the same 'material' clogged the outflow. With rubber gloves on and a bucket below the outflow I rammed the same hose up into the tank. As soon as it started flowing I pulled the hose out and closed the gate valve. After that it drained OK but just to make sure I filled the tank a few times and flushed it out.
I DON'T EVER WANT TO DO THIS AGAIN!
So I bought a backflush attachment and another gate valve. The extra valve will (in theory) allow the backflush water pressure to dislodge the clog and not risk another spill.