This is just my version - Daniel has already made an excellent correction.

Annoyed by My Puppy

I was annoyed by my puppy today. In fact, I was furious when I saw my jasmine leaves scattered all over the floor. Of course he got the punishment he ought to derserved.

You needed some ''link'' (in fact) to move from annoyed to furious. ''Extremely crazy'' was a bit vague - you made yourself sound insane, but not necessarily from anger.

Describing jasmine leaves as ''set'' makes it sound as if it were carefully done. Scattered or strewn are the verbs you need.

He is a dog about three months old. He used to live with His last playmate was a cat, which I had sent to another home a month ago. So it is possible to find some feline nature in him, such as eg. playing with food, or stretching his claws.

Well, we already know he's a dog. ;)

..., which I had sent... - you need a non-defining relative clause here (use a comma and which), plus that action (sending) happened earlier, so you need past perfect.

Now, he is experiencing going through the teeth-grinding period. Some of the furniture has been bitten. That's forgivable. But my poor jasmine - it had just survived from the cold.

Again, perfect tenses are needed here: an earlier event which describes a later situation.

So I guess he won't do it again?

Annoyed by puppy

I was annoyed by my puppy today.I was extremely crazy  angry when I saw my jasmine leaves were set all of the strewn all over the floor. Of course he got the punishment he ought to derserve. deserved. 
He is a dog about 3 months old. He used to live with a cat that I sent to another home a month ago. So it is possible to find some feline activities from him he has some feline habits . eg. playing food, stretching claws.
Now, he is experiencing the teeth-grinding period. Some of the furniture was were bitten. That's forgivable. But my poor jasmine, it just barely survived from the cold.

These are all minor corrections, hope they help! Good stuff. And sorry to hear about your jasmine. What was his punishment?