You already have full control over the positioning of items in Super Tiles, but the tile itself is going to clip any content to keep it within the bounds of the tile. As such, getting CSS control over the individual items is unlikely to help in this particular situation.
In theory, that effect can be created without making an item fall outside the bounds of the tile though. To achieve it, the tile itself would need to be full transparent and a ‘background’ would need to be placed to make it look like the tile background to give the effect that an item was ‘off the canvas’. You could probably do this with Custom CSS, but you could also do it by uploading a custom icon that mimics the background effect and then position it and scale it as the lower most item in the Super Tile to mimic the effect.
Personally, I think this level of customization is probably best suited for a Custom Tile, but of course that would require the necessary HTML+CSS skills. If you wanted to poke around, the Open Weather custom tile could be a good starting point to poke around with.
In the editor, the tile appears to have a grey background, but when you add it to your dashboard, you could set the tile background to transparent and it would look like the icon was hanging off.