The command Divide pipe in the right-click menu divides an existing pipe into two parts, where you point at the pipe and place a node in the division. The command then continues as a draw command so that you have the opportunity to directly draw the pipe which connects at the division. However, you have the option of terminating the pipe both with a new node and to an existing node or an existing pipe by also dividing that pipe!
Make sure that you have zoomed in sufficiently when you have to select a pipe or node so that the snap function does not select anything in the background map.