With whom does the US have the largest deficit using the trade in value-added (TiVA) methodology?
The OECD provides value-added trade statistics from 2005-15. The table below, compiled by the Federal Reserve Bank of St. Louis, shows the U.S. trade balance in 2015 for several major trading partners in terms of gross trade and value-added trade.
Using the trade in value-added methodology, the U.S. trade deficit with China is reduced by 13 percent but still the largest.

Another figure that shows the U.S. trade balance from 2005-15 with several major trading partners in terms of real gross trade and real value-added trade.