Your biggest problem will be moisture. That's why firewood needs to be seasoned for 12-24 months before you burn it. Moist grass will burn shitty, make tons of smoke, and potentially pop hot embers out of the pit and start a grass fire.
Your best uses for grass clippings will be composting, or using as mulch. Throwing green grass in your beds has the danger of setting grass as a weed in (even then, my wife still does it, and she's a better gardener than me) but it will work best if you can dry it to a straw yellow first.
I've had good results composting/aging grass with this bin: https://www.gardeners.com/buy/three-bin-wire-composter/40-280.html
No reason you can't build one as well, if you are willing to put in the time.
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