There is a cryptography technique called Public Information Retrieval which allows you to do just that: Send an encrypted query to a server, let it perform some operations on your behalf, and send you an encrypted query result. The server neither knows the contents of the encrypted data, nor the content of the query, but you have your result nonetheless.
The intuition is that there exists a sort of "black-box" operation which some cryptographic techniques can use. For example, if I have two encrypted bits a and b (where I can't tell what a and b actually are), I can still perform the operation a xor b. The result is encrypted, and I don't know the actual operands or the result, but I know that what came out is indeed the encryption of the xor of the encrypted bits. Such cryptosystems are forms of "Homomorphic Encryption".
Using this, we can then give the server a search term thus encrypted and, using the black-box opertaion, have it do some set of operations which will reveal the result. The server will execute the exact same set of operations independent of the search term, so it knows nothing (and needs to know nothing) of the search term contents. Of course, this implies that the server has to operate on every element of the encrypted data to do its job, but that's the fundamental tradeoff. If you're willing to accept that, and the additional computational overhead, you can design such a system.