Check out the new footage we obtained showing the massive whale's body being mutilated by an excavator -- definitely not for the faint of heart or stomach -- but a group of beachgoers found reason to hoot, holler and celebrate the process.

The removal was coordinated earlier this week by the National Oceanic and Atmospheric Administration -- also known as NOAA -- along with a local marine lab.

The beached whale was first spotted Sunday evening, and reportedly still alive before dying the next morning, when officials quickly attempted to move the decaying corpse.

This video gives you a closer look at the initial attempt to move the massive mammal, as several onlookers record the scene.

Not surprisingly, some locals were disturbed by the crowd's reaction, and a rep for PETA tells TMZ ... "With the planet’s oceans being trawled barren, the death of any aquatic animal is a high-stakes tragedy, and PETA urges everyone upset at the sight of this beached whale to throw all sealife a lifeline by going vegan."

However, as graphic as the removal is, PETA has no issue with NOAA's process ... telling us it's "standard operating procedure."

The city of Venice was forced to issue a no-swim advisory at the beach due to the carcass -- which might be one reason for the cheers.

Researchers cut into the whale's corpse on Monday, causing blood to leak into the water. Translation: the bloody scene could've attracted sharks to shore, endangering swimmers.

BTW, this whale tale isn't nearly as gruesome as a similar situation that went down back in 1970 ... when a Pacific gray whale washed ashore in Florence, OR. That carcass was blown to smithereens with dynamite, and the end result was beyond explosive.