Could a tree be felled with one slice?

Maybe if the tree is very small and the blade is very sharp.

only in films.
https://www.youtube.com/watch?v=OeuoJ6Ic5As

Otherwise a very old dry tree can be cut in one swipe.

My instinct is to say yes, with enough force this should be possible. I’m no physicist, but I suspect the force required is going to be exponentially related to the diameter of the tree as well as some coefficient to account for the moisture level of the tree, species, etc.

Imagine for example a cruise missile with a large axe head traveling at crazy speeds slamming into a tree. I would think it could cut clean through it like a lawnmower blade through grass.

The steel on your blade would need to be high quality; perhaps Demascus steel. The blade would need to wielded by a strong arm with a steely aim to match his blade, but yes, it’s possible.

Since the OP didn’t specify how the blade would be wielded, I will say yes. Using a very hard steel, in a very slim thickness, that being VERY sharp, and propelled at very high speed by explosives.

1)
Here’s an obscure bit of first-hand knowledge for you. At age 20 I lived near New Orleans and my roommate worked at a company which provided blowout preventers to off-shore drilling platforms.

As the name says, blowout preventers close off an oil well drill hole if pressure is forcing fluid up to fast. Their are various kinds, depending on how quickly and thoroughly the brakes need to be applied.

The extreme is the blind shear ram. It slices through the drill pipe and any drilling hardware inside, instantly capping the well.

Stick your tree in one of those and voila!

2)
Here’s how logging companies do it (not in one slice). They have a crane/tractor with a complicated cutting head. It cuts logs in an instant with a chain saw, and then de-branches them. Fascinating. Youtube – 10 Largest and Powerful Forest Harvesters in the World

Not usually. In general, if we’re talking about a human swinging the blade, only a pretty weak and/or thin tree, but it’s possible if it’s not a thin weak tree.

Also it’s not just about strength, leverage, and blade type and quality – the angle of the stroke matters a lot. When chopping with the same arms and axe on the same wood, some blows may sink in, while others do little, or even bounce.

I would say maybe. It would be a matter of force. I have seen a tree felled with a bolt of lightning…a single blow. The unknown is if the handle and/or head of the ax could withstand the blow.

No.
A sapling is too tender and pliable to be cut like than. It just bends and gives way to an cut that is not a single flat cut.
A mature tree would take too many cuts to weaken the fibers enough to fell it.