There are two parts to this question, to which I am answering you as below:
1. Service tax: Under the service tax laws, in case of import of service, the service recipient (in this case your company) is liable to pay service tax @ 10.3% on $ 10,000 (converted at an appropriate exchange rate). This is popularly known as the Reverse Charge Mechanism.
2. TDS: In this case, I am assuming that the Chinese service provider will still want $ 10,000 since he will not be concerned about Indian tax laws about TDS deduction. In such a case, Section 195A of the Income Tax Act will apply, wherein the sum of $10,000 will have to be grossed up to include TDS portion and then TDS deducted, so that the net figure remains $10,000. That is to say, $10,000 / (1 - 0.1) = $10,000/0.9 = $11,111.11 on which TDS is deducted @ 10% to get back the net amount of $10,000.
Hope this clarifies the position.