Can the same couple marry each other again in Mexico as well as in the US?

It is not clear from your question what immigration-related steps you are trying to achieve. Depending upon such details as your and your fiance's immigration status, immigration-related goals, current location, etc. there may be significant advantages or disadvantages to marrying in one country and then having another marriage ceremony in the other country. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant details, could advise you about these issues.