Cesium atomic clocks are not radioactive, nor are they based on radioactive decay. The isotope used for cesium beam atomic clocks is natural and stable Cs-133. The clock is based on an ultra-precise energy transition near 9.192 GHz.

You may be thinking of the nasty radioactive isotope Cs-137, which is unnatural and often a byproduct of nuclear tests or accidents.

It's not unlike Carbon or Potassium; Carbon 12 is the safe stuff, the rarer Carbon 14 is radioactive. Potassium 39 is the safe one and rare Potassium 40 is radioactive. Which is why bananas are slightly radioactive:

https://en.wikipedia.org/wiki/Banana_equivalent_dose

You can make a cesium clock radioactive by placing a banana on top of it. See page 1, 36, 37 of:

http://leapsecond.com/ptti2020/2020-PTTI-tvb-Atomic-Timekeep...