Almost all DIY stores have 'tile saws'. Looks a bit like a 'junior hacksaw', but a bit bigger. Blade is thin and round, with bits of carbide stuck all over it. It your vase is porcelain, you might have a job cutting it.
Theres also a type of hacksaw blade that has a similar carbide coating instead of teeth that does the same thing. You'd have to look for one, as they're less commonly available.