Does it say in Deuteronomy if you see your neighbor working on Sunday you have the right to kill him?

Yes it does.

Exodus 31:15

This is is mistranslation of the original text. The Bible has been translated numerous of times and as you can imagine this leads to different meanings.

The original text reads: "Six days shall you do work: in the seventh day is the sabbath, the rest holy to the Lord. Every one that shall do any work on this day, shall die."

Now the phrase is powerful in it of itself, but it does not state that you can kill your neighbor for this transgression.