[Vuejs]-Vue: splice does not work on the current element

Rather than indicate the index by this.daySelected.indexOf(object), try to indicate directly from the v-for.
You maybe iterate the daySelected array using v-for as follows:

<div v-for="(obj, index) in daySelected">
...
// use `index` to pass as a parameter of the `splice` method.
... deleteObj(index) ...
...
</div>

<script>
...
  methods: {
    deleteObj(index) {
       this.daySelected.splice(index, 1);
    }
  }
...
</script>