by dropping all of the sounds except T'S. "T's great to see you." 

T'S以外のすべての音を落として"T's great to see you."

It is great to see you. Or "T's funny." 

あなたに会えて嬉しいです。または "T's funny."

That's funny. Or "What's going on?" or "T's up?" What's up? T's up? 

面白いですね。または、"What's going on? "や "T's up?"どうしたの？T's up?

And there's also "T's go  come on, hurry up." Let's go. 

また、"T's go come on, hurry up. "もあります。行きましょう。

It's, that, what's, let's  can all be shortened to "T's"

It's、that、what's、let'sはすべて "T's "に短縮されます。