If I send BTC from Jaxx will it give me both BTC and BCC Just want to know if Bittrex supports both blockchains, Bitcoin and Bitcoin cash, when importing from a Wallet like Jaxx
Bitcoin and bitcoin cash are two separate networks, if you send a tx on one network, it will not affect what happens on the other network. If you are using Jaxx, your wallet will show separate btc and bch balances in the app. 

To deposit both btc and bch to Bittrex, you will not to get a btc deposit address from Bittrex and send btc to it. And then get a bch deposit address from Bittrex and send bch to it. 

That said, I am unsure if Bittrex supports bch right now. If they do support it, the above will work. If they do not support bch, then obviously you cannot deposit a coin they do not support.