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.
To remove the signature from Gmail you have to follow some steps.

1. First click on settings on the top right corner of your Gmail page.
2. Then click on the lab tab after clicking to the lab tab you find signature tweaks and enable that option by selecting the radio button.
3. Then click on the save changes buttons to save the changes made to the lab setting.

By the above process you can remove the signature from Gmail.