2001 SUZUKI ESCUDO (GRAND VITARA). My vehicle can't slow down after drive 70 -80 km if I slow engine off and cant start up without accelerating.

no engine stated, and is an engine question.
G16,J20, or H25?
1.6l, 2.0L or v6 ?
my guess, is you removed spark plug wires and put them back out of order, never do that, always change wires 1 by 1.
or the firing order will be wrong, (cops excepted, coil over plug)

how many coil packs do you have.
1
2
4
6?
we cant guess any of that.

clean clear , anon, double post, and still no car named,
nor real engine.

one of these?, sorry cant guess that or the engines.... ever.-
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hello and greetings. you did not say what driveline options
were purchase when car was new. so, can not answer.
but if car is PT 4wd, I can. if not get it fixed, by any 4wd shop.

the car is full time 4wd or AWD ?
PT:
the Part time 4wd must not be driving on dry pavement.
so drive to dirt or grass or ice and then shift back to 2wd

there is a TSB from Suzuki on wind up.

exceptions?
sure , the 2004 options statement here. and the rules for PT 4wd.
http://www.fixkick.com/part-time-test.html

Suzuki Grand Vitara/Escudo -full-time 4WD using limited-slip center differential, off-road 4WD with selectable center differential lock and low range transfer case 4 mode (4h, 4h lock, 4l n), traction control and electronic stability control
Suzuki offered as an option AWD for Grand Vitara's in 2004 (XL7 too) Some Suzuki AWD you can not use lock on dry pavement, so read the operators guide carefully.

suzuki sells the operators guide if lost,
$4 day pass
$25 for full pdf.

https://suzukipitstopplus.com/Products/1042-2004-grand-vitara-owners-manual.aspx

Put seafoam for cleaning system go to auto zone they will tell you.

If the engine starts with a good RPM but does not move when engaged in gear then it is possible that the CLUTCH is faulty and needs a change as it is slipping.
If there is no higher RPM when the accelerator is pressed then the engine needs a tuning. The electrical section for ignition must be checked specially the timing and also the fuel supply and pressure.

the catilaic converter is clogged.

check front brake rotors sounds like there warped..or it might be in your drive shafts check for looseness

I dont think you have an head gasket problem.Check that your therostat is working.Try running the engine without it.Or replace it.I would like to now a little moore about this problem,You dont give enough detail on it.

If everything is the same - yes I would say check with Suzuki dealership. BUT in most cases the service department and the parts department will say no because they have different part #s. But if you have a good parts man he will do his homework to get the sale.

I will assume you have the same thing as in a Suzuki Grand Vitara :
N : Neutral : use this when you tow your vehicle.
4H : Use it in normal road conditions, highway, etc.
4H Lock : Use it on offroad, snow, sand, ... etc
4L Lock : Use when you are stuck on snow or sand, BE CAREFUL, this mode is only for difficult situations, do not exceed 25 MPH, and do not use it in normal conditions.
Hope this help.