Zucchini plants can get very big! My understanding is that you can take some of the leaves off (you often want to do this to give the plant more sunlight) but shouldn't cut any stems. I imagine @CathM would know more...
My understanding of zucchinis, and I have never successfully grown one so you know take all this with a grain of salt, is that they will die back with the colder weather (depending on where you live, obs).
They can get to be really long plants/vines, and that looks like a really small planter box to grow one in (given how far they like to spread).
Hmm good point. I might actaully then just remove it and plant something else there for Winter
Yeah ditch it now and plant something else there. Make sure to give the soil in that bit a bit of love before you plant something new!