My W-2 has box 12 with code W filled in for my HSA from work. Later on, it asks me to enter my 1099-SA form. I did, and it said I overcontributed to my HSA. How do I fix?

Go back through that interview, and if all the contributions were made through work and reported on your W-2, don't enter that amount a second time in the interview. 

So should I just not submit my 1099-SA?

You will enter your 1099-SA. After you enter the HSA distributions from the form, you'll be to enter any contributions you personally made- see @KrisD15 's screenshot.  There, do not enter any contributions you made via payroll.  This will double count them because they were already reported on your W-2 in Box 12 Code W. You also should indicate that the amount withdrawn on the 1099-R was used for medical expenses (if they were in fact used for medical expenses, otherwise it is taxable.)