I think you'll get better responses and more attention if your questions include code demonstrating your own attempts to find an answer, rather than asking others to write the code that you need. Not just because people don't want to feel like their doing free work, but it also becomes much more difficult to answer.
For example, even though what you're trying to do is pretty basic javascript, there are dozens of different ways you could solve it. Here's a quick working answer for your question (using jQuery):
<script>
$(document).ready(function(){
$('select[name=main_dropdown]').bind('change',function(){
if($(this).val() == 'Option2') $('select[name=secondary_dropdown] option[value=Option2]').remove();
});
});
</script>
<select name="main_dropdown">
<option value="Option1">Option 1</option>
<option value="Option2">Option 2</option>
</select>
<select name="secondary_dropdown">
<option value="Option1">Option 1</option>
<option value="Option2">Option 2</option> // Let's say i want to remove this option tag if Option2 in main_dropdown is selected.
<option value="Option2">Option 2</option>
</select>
See it in action.
That said, this solution is incredibly brittle. It'll do what you want in this case, but isn't a very good solution if your relationships change, or code gets more complex, etc. Without example code, it's impossible to tell what criteria you're using to target the options and remove them, so it's impossible to do you much good.
I recommend starting with the jQuery library, which has some great Tutorials. You should be able to solve problems like this on your own pretty quickly if you give it a shot. If your code ends up not working and you don't know where to turn, fear not -- I'm sure people here will be happy to help you out.