Make sure the manifest file for your app contains following permission entries then you can use the code given below to delete a file from external storage.
<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
Code for Deletion
File file = new File(YOUR_FILE_PATH);
boolean isSuccess = file.delete();