Who was the first person to die exploring caves?

Frankly, no-one really knows because it depends on your criteria and the records available. A few intrepid souls tried to explore caves back in the 17th, even 16th Century; and metal-ore miners broke into caves from their mines, from time to time. It's entirely possible some of these people met their end underground, but mining was so dangerous it would probably have been recorded as a mining accident, and then rather scantily.

Of modern explorers, in caves to explore out of curiOSity, I suppose you could count a 19C quarryman called Joe Plumley who died in a vertical cave the quarry had opened up in Burrington Coombe (Somerset, SW England). None of the team were cavers as we would know then now. His work-mates lowered him on a rope but managed to break his neck in trying to pull him back up. The hole was covered over and is now lost, but was near the geological feature now known by the famous hymn that it inspired, "Rock of Ages".