How to eat Rambutan?
Wether or not the stone of a rambutan comes out cleanly depends on the specific variety of rambutan: 

There's freestone and clingstone ones. The stone of the freestone just pops out, the clingstone ones, well, cling to the fruit. The only option for those is to either try to clean it, make a mess, waste fruit, and fail, or to just pop them in your mouth, suck and chew of the flesh, and spit out the stone.

In other words: 
If you want to clean them nicely buy the freestone ones. Problem is: I've never seen rambutans actually labeled as such, at least not where I live, and they're not often available (lychees are more easy to obtain). Maybe it's different in other countries, but over here, it's impossible to tell which variety you have, without trying one.