In the anime, it seemed Amakusa overloaded the magical circuits in his right arm & cut it off to quickly cast his technique. The same appears to happen as well in the manga. This sort of matches the description in FGO where he overloads the magic circuits in his NP Arms, but doesn't need to cut off his arm, which leads me to think that cutting it off is in order to quickly cast his technique. And, the fact that Higashide provides this little explanation on a tweet leads me to believe that this was somewhat anime original or wasn't explained in the Light Novel.
Also, in the anime, after Big Crunch took most of La Pucelle's flames, the black hole exploded, which partially damage the Grail and Amakusa as well, seemingly enough. But, in the manga, Amakusa wasn't hit, it seemed, and the flames still managed to damage the Grail
But, in the manga, it shows how destructive La Pucelle is when the Grail is just "singed" to put it mildy, while being absorbed by Big Crunch.
Just noting somendifferences between the anime and manga