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"She took the job at her friend's expense."

1. Her friend was replaced by her. (It was her friend's job)




2. Her friend helped her to get the job.

Which one is correct? Thank you.

To answer your question,

Mary took the job at her friend’s expense.

could mean your #1 choice, but more likely

1a. Mary and her friend John applied for the same job,
and they were the top two (or the last two, or the only two)
candidates (applicants) —
and there was only one opening (i.e., one position or one job). 
Mary was the employer’s first choice, and John was their second. 
Mary took the job, and therefore John was not hired.

It could possibly be some other (but similar) scenario. 
No English speaker would use the sentence to mean your #2 choice.

at the expense of TFD

Fig. to the detriment of someone or something; to the harm of someone
or something.

From the sentence: "She took the job at her friend's expense," all one can assume is that her friend was harmed or offended and the action did not benefit the friend. It would go against this idiom to state the friend was helping her to get said job. More context would shed light on the nature of the harm and the nuances of their relationship.

As in: "He had a good laugh at the expense of his brother", at best we know that the brother was the part of the 'laugh'. The extent of harm and detriment are determined by the context of the event.