Yes, there is.
Let's first look into the documented way of setting up a knoppix image:
http://knoppix.net/wiki/Knoppix_Remastering_Howto documents the process.
Like with many Linux distributions, you set up an initial installation in a chroot directory, then create a bootable image from that.
Because current knoppix is based on debian, I bet the process is a bit more modern then described in the wiki above, and can just be triggered with a single debootstrap invocation, but I haven't found one (only older docs).
But the good news is that it's really just a debian based distro - so the process is exactly the same. You would just get a full list of installed packages, use apt source to get all the source packages, then for each package, use apt-get build-dep to install the build dependencies, debuild -b -uc -us to build the package from source, and finally place all the binary packages into a directory that you specify as package source during debootstrap.
In essence, you'd be doing a source rebuild of a significant part of debian. I don't know whether that's worth it - debian is very good about reproducible builds and all the packages are checksummed, so that randomly picking packages, rebuilding only these from source and comparing the checksum should yield the same level of trust as building everything from source. Just that you can use debian binary packages, which reduces the build effort from days to minutes.