If you know the CellLabel of the output cell you are interested in deleting then you can do that with code of the form (say it is the 4th output cell):
NotebookFind[EvaluationNotebook, "Out=", All, CellLabel];
This assumes that this code is executed in the notebook in question. Based on this example you could create a small interface that does this in a variety of ways depending on your needs.
But, if all you want to do is to suppress the output of a particular cell, then of course, just append a semicolon to the last expression in the cell.
Other things you may want to look into are $Post, CellEvaluationFunction, and CellEpilog and other functions related to them.