I'm updating the script but the execution log doesn't update Any idea?

The execution log will not update when you update the script. Entries will be added to the execution log when you run the script and call a logging method or throw an error.

I'm calling the logging method But I see the previous logs again and again

Many thanks, their tricks didn't work for me.

I had this recently with a Suitelet - try to change the logging type on the line of code to error or emergency - this worked for me, as I was not getting debug logs