how to travel by road from mexico to belize city?

You DO know that much of that road is not really a road and little more than a path. You MAY make it on a motorcycle, but it's impassable by car... even a 4WD can't make some of those mud holes.

Even if you managed to find some kind of vehicle that COULD make it... you will still have to deal with the BANDITS that inhabit that area. If you are crazy enough to try to make that trip, be sure you say your good-byes to all your friends and relatives because you probably will never see them again.

homie is right
there are alot of roads that are one way than quickyl change into the other way
and road that if you dont know about youll probably fall off a cliff
seriously
its not USA its the rest of the world and the rest of the world dont have freeways like we do ...people are amazed at our roads and freeways
i say get some one who knows what hes doing even then it can be scary maybe a tour bus or something
but yea your a mad man if you think you can pull this off

The Northern highway between Belize City and Chetumal, Mexico is a very good, paved, two lane highway that accommodates high speed luxury buses every single day. I have been on that highway and a car can certainly make the trip.
You didn't say where you were in Mexico but you can easily drive from most anywhere in the country to Chetumal then south to Belize City.

Quintano Roo (Yucatan Peninsula) to Chetumal and across the border, and your there...the Highway is excellent. Getting to Quintana Roo can be a challenge.

You will have to go to Chetumal in Quintana Roo state, it's about 15 minutes to the border, than you take the northern highway and you have to pass Corozal and Orange Walk to get to Belize City, the highway is in pretty good conditions, the ride from the border to Belize City is about 2 and a half hours. You can get to Belize City by car, any type of car or by bus.