Can I say I'm cute to death?
As I say above. I know we can say I'm scared to death about something which express someone is very frightened by sth.
If I want to express something make me feel exceedingly cute? Could I say I'm cute to death?

By the way, I have another question. I read a article today. It says at wedding, there is such a phrase in the vow. 'Till death do us part.' If the word part is replaced by apart will be very out of fashion and could I use tacky or vulgar here to replace ' out of fashion?

Question

Can I say I'm cute to death?
As I say above.  I know we can say I'm scared to death about something which express someone is very frightened by sth. 
If I want to express something make me feel exceedingly cute? Could I say I'm cute to death?

By the way, I have another question. I read a article today. It says at wedding, there is such a phrase in the vow. 'Till death do us part.' If the word part is replaced by apart will be very out of fashion and could I use tacky or vulgar here to replace ' out of fashion?

Answer

"cute" is a word which you would rarely use to describe yourself, perhaps except as a joke. "That baby is cute - look at his lovely face!"  "I like that girl - she's really cute (sweet, nice, attractive).

If you wanted to say something extreme, you could say "He/she is so cute (that) I could die!"

In response to your second question, "part" here is a verb which means "separate"  - "until death separates us".

Answer

“Scared to death” is an idiom.  The meaning of an idiom comes from the phrase, not the individual words.  Generally, words cannot be substituted in idioms at random and still have the idiom retain the same meaning.  Your example, “cute to death” would be completely meaningless in English because, grammatically we have no such idiom using those words.