If I had one million dollars, and in a fit of insanity piled them up and set them on fire, how would it affect the economy?
Well, in the immediate short term, I have one million fewer dollars, and am poorer. The money supply has been reduced by one million, so all remaining dollars are slightly more valuable. (Not much, there are a lot of dollars. What previously cost $1 now costs 99 cents.)
But in the long term, if a lot of people do that, the expense of printing dollars will start to add up. It costs about 2 cents to print every bill, for a total of $200 destroyed in my hypothetical bonfire. Pennies actually cost more than a penny to produce (currently 1.4 cents and rising), but the government mints them at a loss because of the need of exact change. The government will not be pleased at having to repeatedly print money.
Although, again, in the short term, they would benefit, as they would own each freshly printed dollar and could use it to their own ends.
It's the long term where this sort of thing catches up to you. An economy that has to constantly throw wealth creating new paper is an unproductive one. The mounting expense eventually bites you in the ass. This is why deliberately mutilating money is illegal, but you're unlikely to be caught unless you're really blatant about it.