We would like our one-year old neutered male cat to poop outside. Will removing his indoor litter box work? If not, any suggestions?

A litterbox is crucial for cats who are indoor and outdoor. You can't skimp on this one. The cat needs a place to go when the weather is unpleasant outside at the very least. If the weather is good chances are, you won't need to empty it much.

Statically cats who go out side die earlier than those that remain indoors all the time. Unlike dogs you can not keep a cat in a yard. Further there are many more cat diseases floating around out there and carried by 'neighborhood cats' than dog borne diseases. But then how many areas have a feral dog population compared to areas with a feral cat population?

He was trained to the litter box, to the litter box he will go. Even if he spends 18 hours outside, he will wait to use the litter box.

Which is a good thing, there are many ground diseases that cats dig up when they potty outside. Thinks like worms, ring worm, these are from the ground, get under the cats claw, the cat bathes itself next thing you know its got intestinal worms. You pet the cat, next thing you know you have ring worm.

Thus your best bet for your pet is to leave him indoors all the time and forget this 'let him potty outside' as if he is a dog.

Being a dog person, I would put the cat outside and leave it.

Keep the box if he is going to be indoors also. If you take it away before he is used to asking to go out he will just find a place inside to go with no box to contain it.