Taxis can bring wherever you want. There is only one problem: they are extremely expensive.
Going from Siena to near Ambra can cost about 100 euro. You have to consider that Italian taxis are expensive. In particular they have special fares for extra-urban routes, as well as for night service. Also note that Ambra is outside the province of Siena, so you can have additional charges.
If you want to take taxis I then suggest you take it from Montevarchi or Arezzo. Montevarchi is closer than Siena and it's in the same province. If you are coming by train Montevarchi can be a good choice, as well as Arezzo.
Instead of taxis I recommend you consider hiring minibus with driver. There are many companies offering this service in Siena. You can ask your hotel if they can recommend someone. Most accommodations have special agreements with one or more transfer companies and can help you having a better price.
Otherwise there is a bus going from Siena to Ambra. It's line SI91 from Siena to Bucine and San Giovanni Valdarno.
I hope these suggestions help you planning your trip to Tuscany. Don't hesitate to come back with any other questions .
I also hope you'll share with us your experience in Tuscany.