No, Fumes and Texan are right. Cutting an active spring raises the spring rate. For a simplistic example: you have a 10 coil spring with a rate of 100 lb/inch. So if you place 100 lbs on the spring it will compress 1 inch, or in other words each coil will compress .1 inches. If you cut one coil off and place the same hundred pounds back on the spring then each coil will still compress .1 inch, but since you only have 9 coils the entire spring will only compress .9 inches. So the over all spring increased to 111 lb/inch.
The reason is each coil sees the full weight of the load plus the weight of the coils on top of it (but that can be pretty much ignored), and will deflect some certain amount. In the above sample each coil will see 100 lbs of weight regardless of where on the spring they are. If you cut a coil the remaining coils still see that exact same weight and will still deflect the same amount, but since there is one fewer coil the overall spring deflects less, thus its rate goes up.
Adding more coils of the same materail, thickness, radius, and pitch will decrease the spring rate a proportional amount. If we add another coil to out 10 coil spring, then the under 100 lbs of load the spring will deflect 11 * .1 = 1.1 inches, so our new spring rate is now 100/1.1 = 90.9 lbs/inch.
Make sense?