If you have the correct permissions in SharePopint, deletion is an option on the tool bar or the drop down menu. I will assume you are looking for a more efficient method of deletion, besides the explorer view.
I have had a similar situation. Where I wanted users to submit their forms, which requires them to have permissions to a common form library to write the form. Yet I did not want others to access their form so I had a process that would monitor the folder and move the files to a secure library (copy and delete) when they were saved (every minute it would check). Once the middleware has processed the form you can delete the form or archive it somewhere. Ideally the middleware could make that part of its process or script them together. An even better solution I have found is the Database Accellerator product from Qdabra which eases the processing of the forms but also allows you to control permisions dynamically and avoid the whole issue I am describing of moving forms to secure locations.
You should be able to access and browse your SharePoint libraries via the folder structure and delete like normal.
http://sharepointserver/site/formlibrary = \\sharepointserver\site\formlibrary
That is how I have manually deleted or setup automated processes.
Hope this helps.