Deleting a user's profile photo via frontend in Craft3
The input name has changed from "deleteUserPhoto" to "deletePhoto" in Craft 3.

Here is my updated working Twig code if anyone needs it : 

&lt;form method="post" enctype="multipart/form-data" accept-charset="UTF-8"&gt;
    {{ csrfInput() }}
    &lt;input type="hidden" name="action" value="users/save-user"&gt;
    {{ redirectInput('profil/'~currentUser.id) }}
    &lt;input type="hidden" name="userId" value="{{ currentUser.id }}"&gt;

    &lt;input type="hidden" name="deletePhoto" id="deleteUserPhotoInput" value=""&gt;

    &lt;input id="profilePhotoInput" type="file" name="photo" accept="image/*"&gt;
&lt;/form&gt;


And my Javascript code : 

$('.delete-profile-photo-btn').on('click', function () {
    var deleteUserPhotoInput = $("#deleteUserPhotoInput");
    deleteUserPhotoInput.val('1');
    deleteUserPhotoInput.parents("form").submit();
});