Is there a version of turnkey-core thats been updated to latest jessie?

http://www.turnkeylinux.org/14-rc1-aka-we-need-you

Also is it possible to modify the core appliance to remove some stuff I don't need? I want the smallest possible appliance as possible.

For this you'll need to have a look at TKLDev.

A nice easy start to install TKLDev and build an ISO.

TBH I think a "mini-core" or "core-tiny" or something would be cool. Let me know if you have any questions.