Please include the airlines.
I'm only interested in direct flights. In particular no flight may be via USA.
Any country in East Asia and Southeast Asia is OK. I'll have a Chinese visa and can enter most other countries visa free or visa on arrival.
So far it seems that Aeromexico flies into Tokyo Japan, Shanghai China, and Seoul (Incheon) Korea. But I'm not even 100% positive these flights are direct.
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.
https://www.flightconnections.com/flights-from-mexico-city-mex lists the following direct flight from MEX airport to Asia:
https://www.flightconnections.com/flights-from-canc%C3%BAn-cun lists the following direct flight from CUN (Cancún) airport to countries that are partly in Asia (Russia and Turkey), but the airports themselves are in Europe:
https://www.flightconnections.com/flights-from-guadalajara-gdl, https://www.flightconnections.com/flights-from-monterrey-mty, https://www.flightconnections.com/flights-from-tijuana-tij shows no direct flights from GDL (Guadalajara), MTY (Monterrey) and TIJ airports to Asia.
MEX, CUN, GDL, TIJ and MTY are the top 5 Mexican airports.
| # | Airport | IATA | ICAO | 2020[1] | % (19/20) |
|---|---|---|---|---|---|
| 1 | Mexico City International Airport | MEX | MMMX | 21,977,268 |  56.31% |
| 2 | Cancún International Airport | CUN | MMUN | 12,259,148 | 51.89% |
| 3 | Guadalajara International Airport | GDL | MMGL | 8,094,115 | 45.40% |
| 4 | Tijuana International Airport | TIJ | MMTJ | 6,310,798 | 29.23% |
| 5 | Monterrey International Airport | MTY | MMMY | 4,994,170 | 55.32% |
| 6 | Los Cabos International Airport | SJD | MMSD | 2,927,987 | 45.16% |
| 7 | Puerto Vallarta International Airport | PVR | MMPR | 2,489,825 | 49.51% |
| 8 | Del Bajío International Airport | BJX | MMLO | 1,377,573 | 49.85% |
| 9 | Culiacán International Airport | CUL | MMCL | 1,373,102 | 44.16% |
| 10 | Mérida International Airport | MID | MMMD | 1,297,308 | 53.51% |
