1. I'm going to cut tall grass around my ancestor's tomb/grave on Chuseok.

2. I am going to worship at my ancestor's grave.

3. I am going to pay a visit to my ancestor's grave.

4. I'm going to visit my ancestor's grave and worship at the grave. Then I will cut grown-up grass around the grave.

(Would yoiu check the sentences and correct any errors? Thank you.)

We don't use tomb in this situation. Other than that your sentences are all correct.