How to split all BibTeX referenced entries from a big BibTeX database to a copy?

BibTool is a command-line tool which allows you to perform various manipulations on .bib files, including extracting all of the entries which are mentioned in a given .aux file.

A reference manager such as JabRef will allow you to save selected entries from your entire .bib database to a new, smaller .bib file. JabRef also allows you to export to many other formats, such as XML, HTML, EndNote, and Harvard RTF.

You could also try M-x reftex-create-bibtex-file if you're using Emacs and RefTeX.