Central Networks said the person would at least have had severe hand burns.
Engineers found a hacksaw embedded in a live 11,000 voltage cable with a lit blowtorch nearby after being called to Creswell late on Saturday night.
A total of 795 customers were cut off, but power was restored after an hour-and-a-half.
"We can only assume they left in a great hurry or they were injured and were dragged away by an accomplice"
Phil Wilson, Customer Operations Manager with Central Networks, said: "The sheer stupidity of cutting through power cables should be glaringly obvious to everyone.
"At the very least putting the hacksaw through the cable would have created an almighty bang and the line would have burned for quite a few seconds, showering them with molten copper.
"The thief left their tools behind so we can only assume they left in a great hurry or they were injured and were dragged away by an accomplice.
"They could quite easily have lost their life. I can't stress highly enough that it's just not worth it."
Crimestoppers is offering a £1,000 reward for information leading to the successful prosecution and conviction of those responsible.
Police in Derbyshire have appealed for witnesses.
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