Remove an option:
$("#selectBox option[value="option1"]").remove();
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<select name="selectBox" id="selectBox">
<option value="option1">option1</option>
<option value="option2">option2</option>
<option value="option3">option3</option>
<option value="option4">option4</option>
</select>
Add an option:
$("#selectBox").append('<option value="option5">option5</option>');
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<select name="selectBox" id="selectBox">
<option value="option1">option1</option>
<option value="option2">option2</option>
<option value="option3">option3</option>
<option value="option4">option4</option>
</select>