The two question/answers from the Frequently Asked Questions section of the official DoD website:
Q. Why does the exercise use the spelling Talisman Saber?
A. Because TS09 is a US led exercise, we have adopted the American spelling of ‘saber’. As TS11 will be an Australian led exercise, we will use the spelling Talisman Sabre.
Q. Does the name of the exercise have any significance?
A. As this is a joint exercise, the Australians provided the word talisman and the US provided the word saber. There is no symbolic meaning in the name.