A motor is an inductor, which attempts to maintain a constant current. When the motor is switched off, the current that was flowing in the motor prior to turn-off must continue flowing. Since the previous power source (the battery) has been disconnected, the only way for current to continue to flow is for the motor to drive that current with a voltage of its own. The voltage across the inductor (motor) will be whatever voltage is required for the current to continue flowing, and if this current must flow through an open switch (a device designed to prevent current flow), the voltage will be very high.
This alone doesn't blow the fuse. Your typical automotive fuse works essentially by melting from excessive current. But, the motor can't make current higher than it was; it's just increasing voltage to maintain current.
However, there is also overvoltage protection in the car's electronics, most commonly in the form of a crowbar circuit:
Here, the LM431 and triac normally do not conduct. However, if the voltage becomes higher than a threshold determined by the designer, the LM431 triggers, in turn triggering the triac. The triac essentially shorts out the power supply, as if someone threw a crowbar across the rails (thus the name of the circuit). This brings the voltage down, and the excessive current blows the fuse, disconnecting the power source and isolating the fault.
The solution is to put a snubber across the motor, providing a path for the current associated with the magnetic field collapse that isn't through the protection circuitry. In this application, the snubber can be a simple flyback diode. I'm guessing that your car vacuum was manufactured in China and was very inexpensive. By the sounds of it, they could not justify the cost of a power cord of significant gauge, so I doubt they could justify a diode, or the engineer to tell them that it's necessary. Alternate solution: buy a less crappy vacuum.