Here's another cover song, where the musicians changed the song so much, it's nearly unrecognizable.
This is GWAR, recorded live playing the Pet Shop Boys. They mash right into a song I haven't heard in ages, the Jim Carroll Band's People Who Died. A song that I know most folks haven't ever heard. They play the second cover more like the original punk version, but change the lyrics at the end to sing, "Oderus died! Died!". RIP Dave Brockie. Also, look up the original if you haven't heard it.
Disclaimer! If you've never heard of or seen the band GWAR, you may be in for a shock, or a treat, depending. NSFW at times. GWAR is what would have happened in an alternate universe where Benny Hill saw KISS and said, "I want to do that, but funnier". They are serious musicians who do not take their act seriously. It's a Parody act. A joke. Please do not get offended and then pummel me.
A Live Cover, audio only. Done before Mash-ups became a thing on Youtube, this is a Perfect version of a mash-up of two songs by two different bands (Diary of a Madman by Ozzy and Lovesong by The Cure) covered by another band.
12 years ago, some dude decided to use the video for Take On Me by Aha to make a cover song by changing the lyrics to match exactly what was in the video. A "Literal" version of the song in the video. So, I guess, in a way, it's more of a Parody than a Cover, but then again, all lyrical parodies are really covers anyway, just with different lyrics.
I tried to find his version of White Wedding by Billy Idol, but apparently those vids are blocked to me.