Too much sugar in soup -- how to make it less cloying?
Removing dissolved sugar from a recipe, as in your soup, practically impossible.

You have two main choices:


Reduce the impact of the sweetness.  Increasing acidity (lemon juice or vinegar for example--since ketchup contains vinegar, vinegar or more ketchup may be most compatible with your specific recipe) may mitigate how sweet the soup seems.  This may or may not work--you would have to experiment, and it could make the soup taste worse worse (the risk being you would then still have to discard the soup.)
If you really like the borsht, and can eat (or freeze) it all:  make a second batch with considerable lower sugar, and combine them.  You will now have twice as much soup, but flavor balanced.