As the Due is not running a operating System or multitasking scheduler the functions get called sequentially. So the behavior is exactly what you would expect.
As you have a Mini Pro, program that to run the Neopixels and use the Due to the more processing intensive animations. A digital signals between the Due and Mini Pro can be used to synchronise the actions of each processor.
To "interrupt" the animation you need to check for the abort signal after each individual image is loaded and "return" from the function, doing this means keeps the display tidy without partial images and the SD Card files get closed properly etc.