From the Admiralty station, can we go to Repulse Bay by Taxi?

Definitely, you can take one taxi from Admiralty Station to the Repulse Bay directly. But the taxi fee will be so high. Because it is about 10 kilometers between the two places.
Actually, you can go to Central first and then walk to the Exchange Plaze through the Exit A. At the Exchange Square, there are buses No. 6,6A, 6X, and 260. The bus ticket costs around HK$ 7.9. You'd better prepare some small money before you get on the bus.