Reducing a city below 0 health with ranged attacks doesn't destroy it. Assuming you want to take over the city, reduce it to 0 with melee units and you will take control of it.
If you really don't want a city, there are two ways to destroy cities (but neither will work here- see below):
The first is to capture the city and choose to raze it. This will reduce its population by 1 per turn until it reaches 0 and is destroyed.
The second is to drop a nuclear missile (not a bomb) on a small enough city (4 pop or less). This will completely destroy it. Using multiple nuclear missiles will reduce the population each time if you hate a city that much.
Note that neither of these will work on City States as they are unrazeable. It is impossible to destroy City States, original capitals, holy cities, or Indonesian spice cities.