My way is not far from the above one (which didn't work for me, sorry), but it is shorter, contains important update on index inside the loop, and some additional demo for clearing script usage (I hope ;) )
JSESSIONID is one of tokens (first or some of subsequent),
thus in order to delete all the tokens including JSESSIONID I would propose to use the following Java script in JSR223 Pre- and/or PostProcessor where you need:
import org.apache.jmeter.protocol.http.control.CookieManager;
CookieManager cManager = sampler.getCookieManager();
int count = cManager.getCookieCount();
for (int index = 0; index < count; index++) {
cManager.remove(0);
}
Example of adding the script to PostProcessor in jMeter
Pay attention: inside for loop here is (0), not (index), that helps to avoid OutOfBoundary exception, because size of the CookieManager instance comes smaller after each iteration.