This silly scenario just popped in my head, and I wanted to verify what would happen:

Let's say Bob the Redemption Paladin doesn't like to kill his foes (so he attacks non-lethally), but for some odd reason, he's attacking a beheadable foe with an attuned Vorpal weapon. He non-lethally attacks the foe, but rolls a 20 on the attack roll. What happens now?

1. The Vorpal weapon's desire to chop heads off takes priority, and the poor bloke loses their head




2. The Paladin's will to spare his foe takes priority, and the foe still has a head after the strike




3. Another outcome

Chopped off

The rules on knocking a creature out (PHB, pg. 198) state:

[...] When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt.

So this is what happens:

1. You make your attack roll, and roll a natural 20.


2. 
   

   Vorpal weapon chops the head off; the description states:

   
   
   

   
   

   The creature dies if it can't survive without the lost head.

   
   

   
   
   

   Is it still alive? Continue to 3, else stop.

   
   



3. You deal the damage and extra slashing damage (only matters if it's a troll or anything else that can survive losing a head).

The head is still chopped off even he is not reduced to 0 HP. Note that the rule says you declare non-lethal damage when the damage is applied. The poor bloke's head is now off, unfortunately.

The vorpal weapon severs the head.

You actually don't decide to be non-lethal before the roll. The decision is made when damage is dealt (emphasis mine):

Sometimes an attacker wants to incapacitate a foe, rather than deal a killing blow. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. 

However, the vorpal weapon doesn't reduce a creature to 0 hit points. It kills them outright (emphasis mine):

When you attack a creature that has at least one head with this weapon and roll a 20 on the attack roll, you cut off one of the creature's heads. The creature dies if it can't survive without the lost head.

As such, rolling a 20 on an attack removes the head before you can even decide to knock the character unconcsious.

The enemy is beheaded

The vorpal effect is not optional

The description for a vorpal sword does not indicate that the effect is at all optional:

When you attack a creature that has at least one head with this weapon and roll a 20 on the attack roll, you cut off one of the creature's heads. The creature dies if it can't survive without the lost head. 

When you roll a 20 the effect happens whether you want it to or not.

Beheading happens before damage/knocking out can happen

The rules for knocking a creature out say:

When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable.

The rules say nothing about giving the ability to negate non-optional harmful effects (such as the beheading effect) only that the creature can be knocked out instead of killed due to the damage dealt to them.

The vorpal effect simply doesn't interact with the rules for knocking out at all. In fact, knocking out happens at the time damage is dealt, but the beheading effect actually happens as soon as the roll is revealed. So the heads would be rolling before the knocking out rules had any chance to even apply.

Use a different weapon

If the paladin wants to avoid killing things, perhaps they should not be using a weapon that beheads its victims 5% of the time.

The creature's head is cut off.

The text of the vorpal sword's description leaves no doubt.

When you attack a creature that has at least one head with this weapon and roll a 20 on the attack roll, you cut off one of the creature's heads.

It's not optional. If this is problematic, don't allow a pacifist to attune to a vorpal weapon: consider it a violation of the pacifist's character to even try to attune to the weapon, or declare that the weapon itself rejects the attunement attempt.

Everyone is assuming the Paladin struck with the blade.

A character can strike with the pommel of a sword to go for subdual damage.

In old-school D&D, subdual damage was basically you tracking all of the damage you normally would have done, but once the enemy reaches 0 they just yeild instead of die.

To RP this out.. the Paladin would be using the Vorpal Sword. They could clearly cut the head off the opponent if they wanted to.

But, instead, the Paladin is doing subdual attacks...

Think of movies when two people are sparring, and one person is clearly showing dominance over the other, but isn't out-right slaughtering them. The Paladin would be swinging the blade and slapping the opponent with the flat-side of the blade. Or they're side-stepping and letting the opponent fall to the ground.

In this situation, all the "Damage" being caused is just ego damage that is wearing down the opponent's morale.

On the final blow, the Paladin chooses to stop the sword an inch from the opponent's neck and tells them to yield. Or, they knock the opponent out with the butt / pommel of the sword.

Unless the actual blade edge of the vorpal sword connects, then no cutting is taking place, and thus no head-severing is taking place.. at all.

And on a roll of a 20... that is the CHARACTER rolling a 20, not a weapon. So, the character (and thus the player) has say in what they're doing.

If they want to spare an opponent, they can.

But, this kind of subdual damage only works on intelligent foes without god levels of morale. EG: you can't do subdual damage on, say, a zombie. Or skeleton. Both of which (old-school D&D) have a morale of 12.. so they're unshakeable and just keep coming at you until you destroy them. But, on a Vampire you might. On a dragon you might. Any type of foe that knows it's own mortality, and could tell if it's being beaten and can realize the opponent is offering them a way out other then death.

Unless the Vorpal Sword is also an Intelligent Sword that has sway over the owner and thus can force their will upon the user.. I would simply RP this as a character that has a massively destructive weapon and chooses to use it in alternate fashion.

IE: I would role-play this instead of rules-lawyering it.. b/c the rules for the Vorpal Sword will tell you a 20 is a natural beheading.. but that's only if the person holding the sword was going for a death blow.