Question: I have defined multiple signatures in Gmail, but want to delete some of them.
How do I do it? I have figured out how to blank them out, but want to actually delete them so that they don't get selected by accident.

Answer: 
Blanking the field out is the only way and gives the result you are looking for. You can only have one signature per email address; not sure what you mean by selecting one accidently.
I tried to remove an old signature in my Gmail settings and can confirm there is no simple way to delete a signature. I think your best bet is to just clear out the old signature or select the No Signature option. Not ideal at all.