Given your example, you want to get rid of the first cell. I am going to guess for the sake of this example that your table will have an id. So that would look something like this:
var table = document.getElementById('tableID'); //There are other ways to fetch HTML elements, but this is the most direct. It returns a table object.
var rows = table.rows; //Create a variable to store the table rows.
row1 = rows; //Stores the first row in a variable.
row1.deleteCell(0); //Delete the first cell in the first row.
Admittedly, this is a very simplified version. If you are removing cells dynamically, you are probably going to have to collect rows and iterate through them searching for attributes: classes, IDs, etc, and then remove them. If you need help with that, I recommend posting more questions.
I hope this helps!