How Do I Stop Vegetables From Growing Into Eachother?

I have a vegetable garden in my home that is about 5 weeks old. I came back from a 5 day vacation and two zucchini plants had taken over the garden and are growing into everything. Not only are the plants very long and viny but their leaves are HUGE. Is it safe to trim the leaves and maybe cut a FEW stalks or will that kill the plant? If that won’t work, what can I do to stop the plants from continuing to attack the other plants?

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