How to remove specific element from Observable<Array<any>>

You can't do it this way since you can't "update" an observable (i.e. it doesn't keep states) but you can react to an event through it.

For your use case, I would leverage the scan operator and merge two streams into a single one:

• one for the initial loading
• another one for the delete event.

Here is a sample:

let obs = this.http.get('/data').map(res => res.json());

this.deleteSubject = new Subject();

this.mergedObs = obs.merge(this.deleteSubject)
.startWith([])
.scan((acc, val) => {
  if (val.op && val.op==='delete') {
    var index = acc.findIndex((elt) => elt.id === val.id);
    acc.splice(index, 1);
    return acc;
  } else {
    return acc.concat(val);
  }
});

To trigger an element deletion, simply send an event on the subject:

this.deleteSubject.next({op:'delete', id: '1'});

See this plunkr: https://plnkr.co/edit/8bYoyDiwM8pM74BYe8SI?p=preview.