Has my apple tree died

Oh dear, that doesn't sound good......I'm no expert, but I'd say that an tree with no leaves is an ex-tree, if you see what I mean lol Have a look at the ends of the stems and try scraping a bit of the bark back with your finger nail to see if it's green underneath. If you can't find any green, then it's probably dead I would think. However, the tree might well shoot again from the base, but of course you wont get fruit for a few years. Has anything happened to disturb the roots? I ask because I would not think that removing a branch (so long as it is not a huge portion of the tree) would kill an apple tree. What would cause sudden death however is altering the level of the soil around the base of the tree or something heavy like machinery being parked underneath that effective compact the soil, thereby damaging the roots. Waterlogging would also do it as would excessive damage to the bark of the trunk.

I do hope he threw the prunings back into your garden adjacent to the location of your tree, otherwise, it is theft.
If the tree dies, sue him for a replacement if he didn't.
Other than that, it is usual for most plants to withstand a 2/3rds haircut, but I doubt he did that much.
I suspect an unrelated cause.

Don't sue your neighbour, quite apart from the fact that you'll end up with someone next door who hates you, you would have to persue your claim through the small claims court, which means you would not be able to claim your legal expenses from him. Solicitors fees are a minimum of £150 per hour, then there's court fees, so obviously it's not worth it.