Assuming you are using Cognos BI version 10.2 or later you can use the Cognos JavaScript API to do what you want.
In order to manipulate prompts using the JavaScript API you have to give each prompt a unique name. For this example they will be named test1 and test2. The test1 prompt will be the prompt you want to deselect when test2 is selected.
Add a HTML item at the bottom of your prompt page and insert the following code:
<script>
var report = cognos.Report.getReport('_THIS_'); //Assign a variable to the report object
var test1 = report.prompt.getControlByName('test1'); //Assign a variable which points to the first prompt object
var test2 = report.prompt.getControlByName('test2'); //Assign a variable which points to the second prompt object
test2.setValidator(validateTest2); //Call the API's setValidator function to assign a function to fire on prompt change
function validateTest2(values) {
if (values && values.length > 0) { //Check if test2 has a value selected
test1.clearValues(); //Call the API's clearValues() function on test1 which deselects all values
}
return true; //Successfully validate prompt
}
</script>
Since we are supplying a custom validation function you may need to tweak the return value depending on if you set the prompt to required etc.
With this script, any time a value is selected in the test2 prompt, the test1 prompt will be clear.