What's the purpose? Is it for communicating? or a signed document?

Maybe the clay composition, the process of firing it and the final product serve as the signature of the company? Also tile can't be burnt while paper can be. Interesting idea.

It seems that 19th-century tile makers sometimes used clay tiles as memo pads. Cawarden Reclaim (who found that dismissal notice) stumbled upon another tile that contains an order list:

    This is an old handmade pan tile, made on 21st July 1802. [...] Reading the information, it seems that this is an order list for the maker. With no paper and pen to hand, the words were jotted down on a freshly formed clay tile, which was waiting to be dried out and fired. This tile was fired, used on a roof, and remained in place for approximately 220 years. 

I imagine that it was like writing a dismissal note on the white board after a heated office argument.

Perhaps it was a joke?

Why do you overthink it? (The article also seems to mystify it a bit): Possibly put a paper on a drying work item and scribed it on paper, and it got imprinted through the paper.

It's amusing to think this was that company's loser boss version of firing by voicemail. New load of tile, you put all the tile on the roof, hey there's one extra, hey there's writing on it, aw what the hell!!?