Is there any website which shows the work of a sculpturer named
"Messersschmitt" (I think the spelling is correct) who in later life
when suffering from Dementia produced many pieces of distorted faces
saying that these distortions overcame the demons within his head?

Hello.

The sculptor is Franz Xaver Messerschmidt (1736-1783).

A web site called "Franz Xaver Messerschmidt's heads" has a gallery of
the artist's sculptures:
http://www.limmat.ch/schmid/fxm/gallery.html
The main page is at:
http://www.limmat.ch/schmid/fxm/index.html

There is another gallery on the web page of Norbert Schmitt:
http://www.norbertschmitt.de/messerschmidt/koepfe.htm

Biographical information is available courtesy of the web page Fine
Arts in Hungary:
http://keptar.demasz.hu/keptar/english/m/messersc/

Here is an entry from artcyclopedia.com about Messerschmidt:
http://www.artcyclopedia.com/artists/messerschmidt_franz_xaver.html

search strategy: messerschmidt, faces

I hope this helps.

Thank you. Excellent response - within 5 minutes of me posting the question.