Hi,
Most likely this is due to a corrupted user profile. It can also be in cases of account name changes, duplicate accounts for the same user etc.
If you review the ULS logs you will see access denied on the user profile picture library which is at the root of the mysite.
To resolve the issue
1. Make sure the service accounts have permissions on the user profile service application. This can be granted by highlighting the user profile service application in central admin and clicking administrators in the ribbon. Once there add the service account
or the user account performing the operation under administrators groups.
2. Go to the user profile service application in central admin > Manage user profiles and search for the affected user profile.
3. In the user profile delete the entry "SPSITEERROR" under personal sites column and also remove the user profile picture.
save changes and now try deleting the user profile again. Should work :)