What to do with very low offer on an item for sale

Why allow offers if you clutch your pearls when a buy is trying to get the best price? You are doing the exact same thing. It's a negotiation if you allow offers. As a retired Navy vet whose been all over the world it's a slap in the face if you don't try to negotiate in some countries. I assume you allow other nations to make offers, unless you say will not ship overseas. You are cutting out those individuals. There are immigrants in America who grew up negotiating. Older immigrants moved here under that mindset. You're telling them to f off and it's through no fault of their own. Some need to get a grip or don't allow offers if you're so easily offended.

I'd response by saying "Here is the lowest I am willing to go: $xxx."  Take it or leave it.  But don't ask for further negotiation.

It’s your item, your listing if you feel it is an unreasonable offer just ignore it 

Simple. Ignore it. 

I will respectfully disagree with the people who say "ignore it". I say this based on my career, where I earned my income on100% commission.  Some have used the term negotiation 101 and given their answer.  I would start with Selling 101 first. How did you determine your selling price?  Choosing a selling price is not based on what others are asking, but on researching what the item you’re selling has sold for in the last 90 days. Now that you know the true Market Value, you can choose your selling price. Personally, I set the price 20% above market value, leaving room to negotiate.
On to negotiations.  I always start by thanking the person for their interest/offer (as you did) and then invite them to negotiate with me.  As in "Thank you very much for your offer. I believe I have priced the xyz competitively; however, do you have any flexibility on your offer?"  No response? Then someone is just fishing, which is ok. Some cultures start with an aggressive offer. Getting any offer means there is interest in what you are selling. No offers is telling the seller that they love their item more than a buyer.