Once user select the channel or value in mgt-channel-picker or mgt-picker, there is no way to clean the selected value on any event using javascript.
I can ofcourse target the 'X' icon and click on it using Javascript, but will be good if this can be handle with graph toolkit. Is there any way?

For mgt-picker you can set the value of the selected-value attribute or the selectedValue property of the element:
For mgt-teams-channel-picker this is a gap in our current implementation. Could you please raise an issue on the repo to track this?