how should this work?
You typically don't dd a mounted filesystem but only an unmounted one, do you? Otherwise you might screw up your new system as data might still be in memory ...
Solution: don't use dd but flash a new image (you may build your own image which you then can replicate).
If it's about the home folder: that folder you probably could unmount and afterwards dd the mountpoint. What you could do likewise in order to keep your data: put your data on a SD card. That card you can easily backup. In addition you wouldn't overwrite when flashing a new image
My 2 cents
How can I build a new image with my own customizations?
I need also root partition, not just home...