[Vuejs]-Not able to remove a user from a table

First of all, you have to pass both department and user in the click event:

<div class="btn btn-danger btn-sm" @click="removeUser(department, user)">
    <i class="fa fa-trash"></i>
</div>

Then, in the removeUser method:

removeUser(department, user){
    axios.delete(`/api/users/${user.id}/delete`).then(response => {
        const index = this.personnal[department].findIndex(u => u.id === user.id);
        this.personnal[department].splice(index, 1);
    });
}