NOT A TEACHER
Since no one has responded to this thread, here are my $0.02. Both sentences don't really work for me. Why is "Company" capitalised? Is the company called "Company"? If not, I don't see any reason to capitalise it.
I would have written it like this: She resigned from both positions because she could not provide her full services to the company due to the large number of other assignments that she had to complete.
I don't know if my sentence really works or not, so your best bet would be to wait for a response from a native speaker and/or teacher.
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