When taping the sheets together, apply plenty of weight, to compress the material and reduce springiness. An extra advantage of casually layered cardboard targets is that they're forgiving of bad throws. My rather heavy key-stock throwing spikes, even when they strike at a steep angle, can be relied on to go through the first few layers of cardboard and then be held in place by friction. A cardboard target must be solidly backed before it can be used. Mount your target on a sheet of half-inch or thicker plywood, or on an old door, or on a backing of planks.
Plastic tape is adequate for fastening the cardboard to the backing, but use it generously.
Even for short half-turn distances, use a target fully thirty inches wide. Other soft materials besides cardboard can be used for light targets. Large blocks of styrofoam work well when taped or glued to a plywood backing. Discarded sheets of ceiling tile, layered two or three deep, can also be used, although they may not last as long as other materials. A tight bale of hay is suitable if you don't mind a bit of shedding.