How to turn froth into juice?
I have the brand of juicer (Champion) mentioned by the OP in comments.  It's a rather unusual design that isn't used by most other companies.  They are somewhat notorious for producing a lot of foam.  I bought it perhaps 15 years ago, but rarely use it for this reason.  (It still has other uses other than juicing.)

Anyhow, the solution I found to this problem was simply to strain the juice through a fine-mesh sieve.  It won't go quickly and will get clogged with the pulp, so you'll need to a take a spoon or something and stir it around to force the juice through.  It takes a long time, but it's effective because the bubbles dissipate when they go through the sieve.  Given the construction of these types of juicers, I would generally just place a bowl underneath and a large sieve in the bowl to catch the juice coming out.  After finishing juicing, you can turn off the machine and then spend 5 minutes stirring and straining to get rid of the foam.

I have seen others on the internet mention success using a French press to do a similar straining action to destroy the foam.  I tried it once but it didn't seem to work as well (perhaps the stirring action within the sieve also assists with the foam).  Nevertheless, it still made an improvement.