How Does Botox Dissipate Inside Our Body?

Dr. Chen has provided a concise review. I would also add that in addition to traveling through the bloodstream, a recent animal study showed that Botox can travel backwards through the nerve to the Central Nervous System. The effect and consequences of this were unknown. 

You are right that Botox, (generically called Botulunum toxin type A) is in theory harmful because it is the same thing that causes botulism poisoning. However, it would take many many times the doses used in practice to do any harm, and I can think of few things that have a better safety record than Botox, which has been in clinical use for 20 years on millions of patients.
To be more specific, the molecule is a protein which is fairly rapidly broken down before it leaves the area into which it is injected.

Dear YNY
The doses of BOTOX injected for cosmetic purposed are extremely small. They have no effect on the liver or kidneys. In fact very little of the BOTOX circulates in the body. This is because the dose used for cosmetic purposes is so small most of it is locally absorbed by the muscle where it is injected.
When BOTOX is used for medical reasons, higher dose are used and these may be associated with systemic effects. However, this dose is orders of magnitude higher than cosmetic BOTOX. Even these products have proven to be very safe.
It is important to be sure that the physician treating you is using a regulated product intended for human use. These products are very carefully tested and monitored for consistently of their dose.
Be aware, bootleg products don't offer this same level of safety. Therefore, only allow yourself to be treated by highly reputable, licensed physicians. It is not worth saving a few dollars when it comes to your safety. Know who is treating you and what they are treating you with.