We have no higher duty to the american people than to pull this off.

本句的no higher... than...并不是表示 既不...也不...。

这是比较级表示最高级意义。句子等于：

To pull it off is our highest duty to the American people.

To do it successfully is our highest duty to the American people.

做好撤侨这件事是我们对美国人民最崇高的职责。

pull off:  informal : to do (something difficult) successfully

类似比较级表示最高级的例子：

How do you feel today?

I can't feel better. = I feel the best.