How do I remove a shared photostream from only one device?
You don't have control to allow only a subset of the photo stream to come to a particular device.

Photostream takes photos from all devices that feed it, and as it's a store that Apple keeps online, if a particular device subscribes to the stream, it gets a cached copy of all messages.

You can take that device out of the stream temporarily or free up other space on the device to allow the stream contents to be cached locally.

In your specific case, you could exit that stream subscription to clear the space and then have the person that owns the stream re-send it to you once you've gotten space freed up on some or all devices that need to subscribe to your collective stream.