I think that the poster is asking how to delete just all of the output cells. In Mathematica (on the mac, there's a similar command on Windows) one just option-clicks on an output cell's cell bracket and then all output cells are selected.
In the browser version of the Wolfram cloud this does not seem to work. It would be a nice functionality to have.
If you access your cloud notebook via the Wolfram Desktop then it does work there.
