What I would do is remove the script tag from the aspx page and then you can use some logic and if you do decide you want it loaded in the C# you can do
Page.ClientScript.RegisterClientScriptInclude("jQuery",ResolveClientUrl("Common/Scripts/jquery.min.js"));
The problem with trying to remove it client side is that if there is any code in it that runs on document ready then it will have already run by the time you go to remove it.
However, you can try getting to it using document.scripts and try the remove() jQuery command. I still do not recommend this. I recommend trying to get to your end result a different way.