Making shorter radio versions of songs to reduce the runtime of a song is a common thing. Here are a few examples for this technique:

"November Rain" by Guns N' Roses
After the calm vocal part the song ends. The complete ending (which is accompanied by Slash on the electric guitar and Axel Rose on the piano) is almost always missing when the song is aired on the radio. The choir sings:
Don't ya think that you need somebody
Don't ya think that you need someone
Everybody needs somebody
You're not the only one
You're not the only one

"Faint" by Linkin Park
Mostly, the radio version does without Chester's growling towards the end of the song. He screams:
Hear me out now
You're gonna listen to me like it or not
Right now, hear me out now
You're gonna listen to me like it or not
Right now

"Never Be The Same Again" by Melanie C.
Mostly, the radio versions miss out on Lisa "Lefteye" Lopez' rap part.

The same thing also happens for music videos, either to reduce the songs runtime or to make it a little more appealing for a mainstream audience.
Slipknot did a similar thing for the song "My Plague" which was released as a single. For the music video, the band used the so-called "New Abuse Mix" which not only is a little softer in terms of the vocals (there are less growls and swear words) but is also shorter than the original album version because it misses out on 1 verse.
A similar thing happened for "Psychosocial". Two passages of the original version of the song had to be cut out for the TV version. In the background you hear a guitar riff while Corey screams "The Limits of the Dead" several times. The special thing about "Psychosocial" is that unlike "My Plague" there also exist 2 versions of the music video - one WITH the part just mentioned and a shorter one WITHOUT it.

Uncut Version: 05.02 minutes
Shortened Version: 04.17 minutes

Difference in time: 45 seconds


The images had to be brightened up a little for this report.

Alternative Footage:
Time Designation: 02.34

In the shortened version, Shawn Crahan throws a barrel in the fire in regular speed. In the uncut version it happens in slow motion.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.39

In the uncut version you now see the scene where the barrel is thrown into the fire in regular speed. In the shortened version you instead see the band performing.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.42

Shot of the band performing. In the shortened version you see the flames in flaring in front of the band - not so in the uncut version.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.52

In the shortened version you see Shawn Crahan a little earlier turning around while playing the drums. In the uncut version you instead see Paul Gray and flames flaring in the foreground.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.55

In the uncut version you again see Shawn Crahan turning around a little longer and playing the drums. In the uncut version you instead see Sid Wilson sticking out his tongue - in his eyes you see a red reflection.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.57

In the uncut version you again see Shawn Crahan playing the drums in slow motion. In the shortened version you instead now see Sid Wilson sticking out his tonge and the red reflection in the eyes. After that you see another short shot of Shawn.
No difference in time.

Shortened Version:	Uncut Version:

Alternative Footage:
Time Designation: 02.58

In the uncut version there's another shot of Shawn turning and drumming. In the shortened version you instead again see Sid Wilson sticking out his tongue and the red reflection in his eyes.
No difference in time.

Shortened Version:	Uncut Version:

New Footage:
Time Designation: 02.59

This scene is only included in the uncut version:
There are several shots of Corey screaming: "The limits of the dead!" He's accompanied by heavy guitar riffs. In between there are a few shots of the band rocking out.
29 sec.

New Footage:
Time Designation: 04.11

This scene is only included in the uncut version:
In the uncut version you see a close-up shot of Corey. Then follow several cuts to the band performing and Corey walking past his band members. Corey screams "The limits of the dead!" twice - again accompanied by a rocking tune.
14 sec.

Alternative Footage:
Zeitindex Shortened Version: 03.48
Zeitindex Uncut Version: 04.31

In the shortened version you see a close-up shot of Paul Gray. In the uncut version you instead see Chris Fehn shouting in the microphone.
No difference in time.

Shortened Version:	Uncut Version: