How delete an item using vuex?

You want to commit a mutation to delete the car

Here is your method

deleteCar (cars, id) {
    this.$http.delete('http://localhost:3000/cars/' + cars.id)
        .then(() => {              
              this.cars.splice(id, 1);
        });
}

Instead of deleteCar(cars, id) you will want to change it to deleteCars({commit}, id)

So your action would be

deleteCar ({commit}, id) {
    this.$http.delete('http://localhost:3000/cars/' + id)
        .then(() => {              
             commit('DELETE_CAR', id);
        });
}

And you have a mutation DELETE_CAR

DELETE_CAR(state, id){
    index = state.cars.findIndex(car => car.id == id);
    state.cars.splice(index, 1);
}

A simplified answer for clarity.

in the template:

<button @click="deleteCar(car)">Delete Car</button>

method in the component:

 deleteCar(car) {
    this.$store.commit('DELETE_CAR', car);
 }

mutation in the store:

 DELETE_CAR(state, car) {
    var index = state.cars.findIndex(c => c.id == car.id);
    state.cars.splice(index, 1);
 }

I see that you're using Axios with Vue, so your request .delete requesst that delete already but in .then you should do something not related to delete or splice,

     deleteCar (cars) {
        this.$http
          .delete('http://localhost:3000/cars/' + cars.id', { data: payload })
          .then(
            //here write what you want after delete
            res => console.log(res);
          )
      }

in .then you do what you need after delete because of .delete request already deleted that part from your JSON data