[Vuejs]-Vuex and dynamic states. Is possible?

Since your keys initially are not declared in data, Vue can’t track the changes. You need to use Vue.set to reactively add properties, see change detection caveats:

import Vue from 'vue'

const mutations = {
    changeOrAdd(state, {key, value}) {
        Vue.set(state.data, key, value)
    }
}