For convenience, you can instruct KWatchGnuPG to clear the log window using → (or the corresponding toolbar icon).
Use this prior to starting the crypto operation that you want to monitor to get only the output from that operation. You can then save the log using → as described above.
Clearing the log discards any previous log window contents. If you are unsure about whether you'll need the current contents afterwards, you should save them to a file (see above) before clearing.