Need to find a new tyre mate.
As long as the tyre is not completely dead (i.e, it’s red on the stats screen) you can repair it with a welder.
Blow the tyre completely? Need to find a new one. That’s the same for all vehicle parts, so make sure you keep your engine, gas tank and windscreens in good repair. You should be able to get away with using a smaller tyre, it’s better than nothing and finding a 13" or 25" tyre in itself is a wonderful find.
Gas tank doesn’t matter that much now, seeing as you can craft one out of a metal sheet. Still, I always have two gas tanks just for extra fuel capacity and redundancy. Better yet, my of my vehicle plans include multiple wheels-- i.e if it would have four wheels, it’d have eight. Four front, four back. Means that you can blow a wheel without careening into the nearest liquor store.
Another handy tip: Scout ahead on unknown roads and (N)ote any trap positions.
As I adventure through towns I usually find trap caches or better yet, landmines. If I wanted to make a hasty exit I certainly don’t want to drive through em.
I actually fell to a nailboard trap once. It was obscured by zombie corpses and me, in my deathmobile thought I’d cleared out the town. Well, I had-- I just hadn’t disarmed all the traps in the neighbourhood. 
Luckily you can still drive fine with just three wheels, because when a survivor builds a deathmobile he DAMN WELL builds a deathmobile that can function with only half the amount of wheels it started with.
