Why check engine light comes on then starts to chug if speed reach 60 or accelerated

There are numerous things that will cause this problem. If the check engine light is on, have the codes checked to see if there is a problem the computer has found to cause this issue. Even without the check engine light on, there may be a code stored. You can also do a visual inspection under the hood for any disconnected hoses causing vacuum leaks. These are the best places to begin with diagnostics

which car? name it and year, all cars vary by year, make and model
and by country, in fact, vastly so.
does it do this hot and cold (engine temp)
does the engine reach and hold at 180 to 200F temperature>?

this is called surging.
is the idle steady, at 800 RPM hot engine?
ever tune up the car,? (called maintenance service points now)

if turbo charged diesel , have the turbo inspected and check the hoses for tight at connections

I doubt it. You should have the computer checked for trouble codes.
It could be a long list of things including low fuel pressure.

Next time the engine light comes on, get the codes pulled and get back to me

run the fault codes first to check for faulty sensors
what you describe indicates a problem in the exhaust in that when the exhaust gas volume reaches a certain level the sensors are reporting it and the ECM is not able to fix it
have an accredited exhaust shop check the cat converter
for failure and partially blocking the exhaust at speed
if it was a fuel pump you would run into problems long before the speed at which it occurs
AT best it could be an EVAP problem with the vent not working properly but I think that it is exhaust related

try the throttle control electronics on the end of the throttle pedal as their is no cable but a electronic reostat control and when this plays up you get the symptoms you describe

The fuel filter is probably full of metal too. (fuel starvation) replace it.

What speed are you going when it chugs?
It could be as simple as a bad spark plug or a spark plug wire/boot grounding out.
When spark plug boots get old, the rubber cracks and lets voltage arc out the side and to the engine instead of through the plug.
This will be most noticeable when trying to maintain a speed of over 40 mph, or under mild acceleration.
The reason for being noticeable at this speed/acceleration level is that the transmission torque converter will be locked, transferring the vibration from any engine miss straight through to the wheels.

This could be a multitude of things but my first suggestion would be to change the spark plugs. They are cheap and can be bought at any auto parts store.