Here's my response to what I think that you are asking:
Once you are done with a particular email item in Gmail, you change the label to 'Trash' or delete it (using the check-box to the left of the conversation). This moves it to the 'Trash' folder. There isn't a way from the Gmail app to empty the 'Trash' folder, that I know of. You can do that from the computer by the 'Delete Forever' button. Make sure that the items aren't in another label as well so that they can be completely erased.
If I have misunderstood, please let me know, but I think that this is what you are asking for.
*Edit* - Items that are put in the Trash folder are deleted automatically after 30 days.