grammar - Subject/Topic/Object

私は犬が殺す // Watashi wa inu ga korosu Means I am killed by a dog

私は犬を殺す // Watashi wa inu o korosu Means I killed a dog

Right? I want an in-depth answer for this if I was wrong.

Answer

Your examples

1. 
   

   私は犬が殺す is very weird semantically, but technically valid. You translated wrong on two accounts: a) it's not in past-tense, b) the function of は is different than what you are thinking:

   
   

   
   

   私は犬が殺す
   Lit. "As for myself, dogs kill me"
   Lit. "As for myself, dogs will kill me"

   
   
   

   
   

   The only time that would it would make sense to say this is if you are iterating through a bunch of different people explaining how they are or will be killed, and then finally you get to yourself and as "as for myself, dogs (will) kill me".

   
   

   However, ネズミは猫が殺す, using the same structure, is somewhat less weird:

   
   

   
   

   ネズミは猫が殺す
   "As for mice, cats kill them."
   "As for the mice, the cats will kill them."

   
   

   
   

   As in -- "(We are talking about a bunch of different things, and moving on to the mice...) as for the mice, the cats will kill them."

   
   

   However, my feeling is that this is sort of an awkward construction in general, compared to using the passive for it.

   
   
   


2. 
   

   私は犬を殺す is totally fine & natural in Japanese, but you translated it wrong.

   
   

   
   

   私は犬を殺す
   "I kill dogs"
   "I will kill a/the dog"

   
   

   
   

   This sentence is not past-tense, which would be 私は犬を殺した.

   
   

The general explanation

You have the general right idea that something marked by は can fall either into the subject or object position depending on what is already in the sentence.

However, what you are missing is that if the は-marked word falls into the object position, the は indicates that there are some other objects being discussed as well.

(Also, I feel like this was perhaps not what you were asking about with your question, but make sure to review your tenses, because you got that wrong with both sentences.)

Technical appendix: contrastive は

A は-marked item can serve either as a subject or as an object. When it serves as a subject, it can optionally have contrastive semantics. When it serves as an object, it must have contrastive semantics.

Critically, in the case は gains contrastive semantics, the thing being contrasted is the entirety of the sentence to the right of the は.

ネズミは猫が殺す

nezumi-ha [neko-ga koros-u]
mice-CONTRASTIVE.OBJECT [cat-SUBJECT kill-PLAIN]
"As for mice, cats kill them... (as for some other animal, another thing kills it)"

猫はネズミは殺す
neko-ha [nezumi-ha [koros-u]]
cat-TOPIC.SUBJECT mice-CONTRASTIVE.OBJECT [kill-PLAIN]
"Cats kill mice... (but cats do not kill some other animal)"

The is to say, something contrasting 猫が殺す is another thing killing. Something contrasting 殺す is just not killing.