I plugged "Mexico, anywhere" to "China, anywhere" for a random Friday in August into Skyscanner, and it only throws up one-stop connections - no direct flights. Ditto going to South Korea, India, Singapore. However, there is a single direct flight from Mexico City to Tokyo (14h on Aeromexico).
On a Saturday, I can see a direct flight from Tijuana to Shanghai, as well as Mexico City to Tokyo again.
The flights are AM98 (to Shanghai) and AM58 (to Tokyo). The AM98 code is used for both Mexico City - Tijuana and Tijuana - Shanghai legs of the journey, but looking at a recent flight map it seems pretty clear it's non-stop after Tijuana. AM58, likewise, does not seem to stop.
Going beyond that answer - if you're happy to tolerate a connection anywhere but the US, there are flights which connect in Canada; however, I think they have US-type transit visa requirements, so it might not be any more help. The long way around via a connection in Europe might be worth looking at in case a cheap ticket via some unusual route turns up; you can (mostly) have airside transit without visas there.