It isn't sugar with the carbohydrates removed; that's like talking about iron with all the metal taken out. Sugar is a carbohydrate, and nothing can change that.
Splenda is a brand name for sucralose. According to the sources I've found (shown below), sucralose is made from sucrose (sugar) by substituting chlorine atoms for three hydrogen-oxygen groups on the molecule. The theory being that the resulting molecule has a similar electrical structure to sugar, so it stimulates the taste buds the same way, as a sweet taste (only about 600 times sweeter!) but it's no longer capable of being broken down by the body's enzymes, so it has no calories and doesn't affect diabetics. Makes sense, I suppose.
According to their hype, sucralose is very stable, and not just in the body: it supposedly has a better shelf life than, say, NutraSweet (aspartame), and survives cooking and other preparations better. They also show a very similar flavor profile to sugar for it. I've not yet (knowingly) tasted it myself, but I'm getting intrigued; maybe I'll get hold of some.
Most of this is from http://ificinfo.health.org/qanda/qasucralose.htm, from the International Food Info Council Foundation (whatever that is), and also from http://www.officialsucralosesite.com/ (wow, what a URL), by the manufacturer. Needless to say, there are already plenty of people out there that don't trust it, as can be seen by the Sucralose Toxicity Information Center at http://www.holisticmed.com/splenda/. Read what you can, educate yourself, and decide what to believe, naturally.