First, install the bibtex-ruby gem.

gem install bibtex-ruby

Then use the citecut.rb script, like so:

ruby citecut.rb paper.tex allcitations.bib > paper.bib

It'll go through the TeX file, finding all commands that contain cite in the name of the command, and extract the contents, splitting on commas.

Then it filters through all the citations in the allcitations.bib file, only keeping the the ones cited in paper.tex (the search is case-insensitive, but for non-case-exact matches, it coerces the BibTeX entry to match the actual cited case).

It then prints all of these to STDOUT, sorted naturally on the citation key. It lowercases the citation type, like @article, or @inproceedings, standardizes indentation, and purges all comments. It is more picky about the formatting than TeX, and only gives token-location (not line number) on parse errors. But it preserves the exact contents of fields, as well as ordering.