My hyundia tucson keep cuting off when i drive the jeep and i have to stop it cut off any time i stop it cut off and when my foot on the brake it move when myfoot is on brake

Possible pilot shaft bushing or throw out bearing going bad.

consider this
when at the stop lights , you will have your foot on the brake as it will still be in drive or in gear and you don't want the car to move
a simple test is to apply the hand brake to stop the car and don't touch the foot brake
if it idles ok but cuts out when you apply the foot brake , replace the brake booster as it has a vacuum leak that is causing the problem
you can do this test in the garage by starting in neutral and allowing the engine to idle , then apply the foot brake
iof it dies it is the booster

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2005 Hyundai Tucson Recalls - Cars.com

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Cars.comLook up all NHTSA vehicle safety recalls for your 2005 Hyundai Tucson, and contact a nearby service center for free repairs.

2005 Hyundai Tucson Problems, Defects & Complaints

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7 days ago - The 2005 Hyundai Tucson has 199 problems & defects reported by ...January 11: Hyundai Genesis Recalled to Replace Dangerous Tires ...

Hyundai Tucson Recalls ' RepairPal

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Other systems that may be affected include: cruise control, push-button start, gear shifter, and Electronic Stability Control (ESC) system. Dealers will replace the brake light switch to correct this concern. ... The stop lamp switch may fail, affecting many vehicle systems including ...

2005 Hyundai Tucson Recall - Learn About Recalls for 2005 ...

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Jack up vehicle, remove wheel, take out bolts holding caliper on. Push piston of caliper in all the way with screwdriver or pry bar. Remove caliper, only doing one at a time as to not push piston of opposite caliper out. Pull caliper out of position, remove and replace brake pads. Install and bolt on caliper, repeat steps for other side. Pump up brakes to get pads against rotors, put wheels on and take for test drive.

sounds like fuel injectors

simple test
ut the hand brake on and start the car
idling ok --good --apply the foot brake-- idling bad --replace the brake booster
check for other vacuum leaks including transmission actuator hose , dash vent controls hoses

TPS or IAC maybe

you are labouring the engine too much for the engine power ,you must keep teh RPM up it is a diesel and they will not develop power like a petrol engine at low RPM ,always pull away in first gear anyway or you will burn the clutch out in no time

your fuel injectors are clogged

i think your exhaust might have a leak which is heating up your oil when this happens the engine suffocates and wants to die.