Sure, here is a Python function that accepts a list of student marks and returns the minimum mark, maximum mark, and the average mark:

def marks_analysis(marks):
    min_mark = min(marks)
    max_mark = max(marks)
    avg_mark = sum(marks) / len(marks)
    return min_mark, max_mark, avg_mark

# Testing the function
marks = [85, 90, 78, 92, 88, 76, 95, 89]
print(marks_analysis(marks))

In this function, min(marks) is used to find the minimum mark, max(marks) is used to find the maximum mark, and sum(marks) / len(marks) is used to calculate the average mark. The function returns these three values.

The function is then tested with a list of marks. The print statement will output the minimum mark, maximum mark, and average mark of the list of marks.