Can ashes be left in Disney World?

Answer 1

Technically Yes they can be but you'd have to be very secretive about it after all there are security cameras & guards around the park, not to mention the hundreds of guests who would see you dumping a powdery substance & alert said guards.
It wouldn't be wise to do it on any of the rides, The Haunted Mansion is the most popular to do it but those rides are cleaned thoroughly constantly so ashes would simply be vacuumed up. If you feel you absolutely have to, you could possibly use one of the landscaped areas or even in the water or in one of the resort areas.
Naturally these places [perhaps not the water] would, like the rides, also be cleaned & cared for on a regular basis so most likely the remains wouldn't stay there for long unless you actually buried them.
If you want to be daring you could release them in the World Showcase Lagoon or if you really want to be daring release them in the water by Cinderella's castle.
Personally if it were me, I'd take a small vile or perhaps a pill bottle with some ashes and stay at a resort with water access, like the Disney Beach Club, Swan & Dolphin, the Floridian or Polynesian and release them in the lakes, or stay at the Campsites at Fort Wilderness at go out after dark and either bury or release them in the woods. Of course remember there is security most likely so you'd have to be cautious.
Possibly the best way to do it would be to get a drink that you can carry around the park, find a secluded spot, mix the ashes with the ice/drink, find where you want to put the ashes, either in one of the Disney lakes or landscaped areas & pour the drink(ashes) there. If anyone sees you they'll think you're simply disposing of an unwanted beverage.

Answer 2

No. If you try to dump Grandma's ashes on the Haunted Mansion ... you'll probably be caught, you'll likely be thrown out of the park, and if you do get away with it, they'll get vacuumed up and discarded the next time the ride gets cleaned (besides which, it's just gross), so don't do it.