How to quarantine or delete infected files with ClamAV?

You can use clamscan with the option --remove to automatically remove all infected file in the scanned folder. WARNING: Files are gone.

clamscan -r --remove /home/USER

Another possibility is to move the infected files to another folder with the option --move=FOLDER, so you can later check which files of them maybe not infected or a virus.

clamscan -r --move=/home/USER/VIRUS /home/USER

See: How do I scan for viruses with ClamAV?

Once the scan is finished, a window should pop up listing the threats. You have to actively select (click on) each threat you want deleted, then click on the delete or quarantine buttons. Simply clicking "delete" without selecting a file will do nothing, which is what you've run into. To select all, click on the top file, scroll to the bottom of the list, and shift-click on the last file. Then clicking quarantine or delete will process everything found. You will get confirmation windows popping up for deleting certain things like .pdf files.