my is an adjective, and adjectives modify nouns, not verbs. So,
Ex: That would be my
killing her.

<noun: gerund>
Ex: That would be my
kill her.

<non-gerundival noun>

Originally Posted by
unregistered Since the word "kill" can used as noun, can I change "killing" for "kill"? If can't, why?
Gerunds--because they have verbal qualities--can take an object as well as adverbs:
Ex: That would be my killing her slowly. 
<gerund + object>
The gerund killing takes the pronoun her as its object, and the adverb slowly modifies the gerund killing.
Non-gerundival nouns, like kill, can also take objects, but they are prepositional in form:
Ex: It's
the kill of the day.

<non-gerundival noun + object>
Does that help?