You are in my sight, so I cannot see the TV!
No, this does not make sense in any normal context. You cannot say this.
As Kate and Ellie have mentioned, what you want to say in this situation is that the person is blocking your line of sight to the TV, or that they are blocking your view of the TV.
In this usage my sight and my view are not synonyms—or, rather, they sort of are, but you don't actually want to say "my sight/view." If something is in sight or in view it means you can see it from your current position; for example, from your current position you probably can see the window, and the other chair, and the doorway, etc, etc. All of those things are "in your sight" but they are not preventing you from viewing the TV.
What you want to say is that the person is hindering your view of the TV. This prepositional phrase with "of" means that you are able to see one specific thing, or not, in this case. Idiomatically, we do not say that someone is blocking our sight of something; we only use view of.
The following are all more-or-less idiomatic, and mean what you want them to mean:
Get out of my view of the TV!
Stop blocking [my view of] the TV!
You are between me and the TV!
Get out of my line of sight to the TV!
That last one is a little less idiomatic but still understandable.
If you say "Get out of my sight" that literally means you want the person to go away completely, that is, move themselves so you cannot see them at all. It does not mean that you want them to get out of your line of sight to some object. And it has the further meaning, by extension, that you are very angry at or disgusted with them, and you do not want them to even be near you. If I told someone to "get out of my sight" and they simply walked around to stand behind me, they would be taking the literal meaning but not the deeper one.