Slate stone question

You might but I doubt you can get much for it as most people don't want to deal with loading and transporting it. Most stone is relatively inexpensive, it's the labor to set it that cost $$$. Also, is it set in grout or on sand/gravel. If grout, forget about it. And is it true slate or a limestone/granite flagstone?

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also it depends on where you live. If there’s plenty of stone around your area it will be cheaper for someone to just buy elsewhere (it will be stacked and delivered for them).

I’d find friends/family/etc and offer to help them remove it in exchange for them hauling it away. If it’s not in a mortar bed you can usually pry it up with a crowbar and flat shovel. Really helps to have a piece of equipment though, something with forks or a bucket