Remove the positive batter cable and the car shuts off

Welcome to 2CarPros.

No, you are opening the circuit and most likely it will stall. I will tell disconnecting the battery with the engine running can damage the alternator. Here is a link that shows how to test an alternator. If requires the use of a volt meter or multi meter.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

Here is a link that shows how to use a volt meter/multi meter:

https://www.2carpros.com/articles/how-to-use-a-voltmeter

Do this and let me know what you find. Also, if you get a chance, describe the symptoms.

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If you find the alternator is bad, here are the directions for replacement. The attached pics correlate with these directions.

First, here is a link that shows in general how it is done.

https://www.2carpros.com/articles/how-to-replace-an-alternator

Here are the directions specific to your vehicle.

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Removal Procedure

picture 1

1. Disconnect the negative battery cable.
2. Remove the drive belt.
3. Reposition the protective boot (2) from the generator output BAT terminal.
4. Remove the generator output BAT terminal nut (5).
5. Remove the engine harness terminal (4) from the generator.
6. Disconnect the generator electrical connector (3).

picture 2

7. Remove the generator bolt and stud.

picture 3

8. Remove the generator bolt.
9. Remove the generator.

Installation Procedure

picture 4

1. Install the generator.
2. Install the generator bolt until snug.

picture 5

Notice: Refer to Fastener Notice.

3. Install the generator bolt and stud.

Tighten the bolts/stud to 50 N.m (37 lb ft).

picture 6

4. Connect the generator electrical connector (3).
5. Install the engine harness terminal (4) to the generator.
6. Install the generator output BAT terminal nut (5).

Tighten the nut to 30 N.m (22 lb ft).

7. Position the protective boot (2) to the generator output BAT terminal.
8. Install the drive belt.
9. Connect the negative battery negative cable.

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Let me know if this helps or if you have other questions.

Take care,
Joe