Hey Michael. I'll try to make this simple, as I am still learning. I'm probably going to explain this oddly, so someone else can correct me if they wish.
'Te' is the direct object. It's who is receiving the action.
Do you know what conjugation means? IF the verb is conjugated, it goes before. Examples:
Te quiero = I want you.
Te veo = I see you.
Te amo = I love you.
quiero te, amo te, veo te. That doesn't make sense!
If the verb is conjugated it goes before!!HOWEVER!!!
If it's
not conjugated i.e. you use the infinitive. Examples:
I would like TO SEE YOU.= Me gustaria ver
te
I am going to call you later = Voy a llamar
te mas tarde.
Do you see the difference? The verbs are not conjugated. They are in their infinitive form (ver, llamar, etc). See, it wouldn't make sense to say:
Voy a llamo te.
NOPE! Because that would be like: I am going to I call you. You can't have two conjugations next to eachother.
UH OH, there's more..
You can also say
te voy a llamar! That means I am going to call you. But all you did was switch the position from the END, to the beginning: That literally means: You, I am going to call.
Did I confuse you? By the way in your example, "matame", that is the COMMAND form of "KILL ME!". If you were to switch it from "me mata", that means, "It kills me". "Matarme" means To Kill Myself. Just think, everytime you see the "r" at the end, is "To [blank]". It's the infinitive.