[Vuejs]-Vue Component control Component instance variable by another same Component

The main issue is your state is stored in the popups instead of the component that holds the popups

For example:

<popup v-model='pop1' />
<popup v-model='pop2' />

watch(pop1, value => {
 if (value) pop2 = false
})

With that said, you can workaround by having your popups emit an open event. When the parent receives this, it can close the other popup.

<popup ref='pop1' @open='$refs.pop2.close()' />
<popup ref='pop2' />

With many menus, it will be best to have a currentMenu property you set. When a new menu opens, you update the current member.

<popup ref='pop1' :value='current==="p1"' @open='current="p1"' />
<popup ref='pop2' :value='current==="p2"' @open='current="p2"' />