You already know that in HTML there is no search option in the dropdown element. When you press any single key on the dropdown then it takes you to the option but not allows you to search whole or particular string.
In PHP, you can simply use unlink() function this removed a file from your server if it exists.
What in the demonstration ?
For demonstration purpose, I create a number of <img> element with Delete Button. When the Button gets clicked then removing the file using jQuery AJAX and replace the <img> source with the default image.