If I changed my tire with the wrong size tire as a spare will that cause my vehicle to stop driving?

If it is a spare in the boot/trunk it will be valid for your vehicle and usually the PSI/BAR pressure is double of the original tyre.

Spares should always be used as an emergency, and repairs to the original should be carried out ASAP. Driving speed conditions are usually requested to be limited to a maximum of 50KM/H with a spare (read the notes on the sidewall of the tyre or in your car manual). The width of the spare is normally thinner.

***WARNING***
If you are talking about a tyre which is smaller in height to the original tyres, whether it be a spare tyre or not. It MUST NOT BE USED. Aside from the potential damage it can cause to your vehicle, the wear to the other tyres, your tyre bearings being damaged, the the axle and drive shaft and suspension load change. It will cause potential loss of steering thus resulting in an accident that as you have types on here, you might have been awake of which if you are in an accident could result in prosecution/felony.