Since spiccato is often learned a long time after the student has been playing with the bow on the string, it can be hard for some students to allow their bow to come up from the string (which is called "off the string").
Swinging the arm from the shoulder joint is the motion for this "brush stroke" type of spiccato.
I usually tell these students to pretend that they are 3 years old. This usually makes them not care if they produce a scratchy sound and gives them the confidence to begin to experiment with the elasticity of the bow.
Here's a file you can download to see the open string exercises I created to begin experimenting with the elasticity of the bow and how it feels to "bump up" to a higher string. My student, Serena, is trying them out in the video below.
Here's a video which has an easy way of feeling and understanding the arm motion, by placing the cello sideways. Bounce the bow on the D string in this way, then put the cello back to its normal position and with the same arm motion, your arm will be playing spiccato on the C string.
I also talk about other aspects of how to get to the higher strings without tightening up the shoulder joint. If you do not have long arms, your shoulder may come forward as you move to D and A string so you must let your torso rotate on the vertical axis of the spine.
I like to use Christopher Bunting's spiccato exercises with my students. They are really fun to practice when learning spiccato. You'll find them in his "Portfolio of Exercises Part One".