1) To make the back button disappear in react-navigation
v5 or newer:
{     
    navigationOptions:  {
    title: 'MyScreen',
    headerLeft: ()=> null,
    // `headerLeft: undefined` should work too
    // `headerLeft: null` should work but could trigger a TS error
}
NOTE:
v6 has an extra option:
headerBackVisible: false
Whether the back button is
visible in the header. You can use it to show a back button alongside
headerLeft if you have specified it.
https://reactnavigation.org/docs/native-stack-navigator/#headerbackvisible
v2-v4:
navigationOptions:  {
    title: 'MyScreen',
    headerLeft: null
}
2) If you want to clean navigation stack:
Assuming you are on the screen from which you want to navigate from:
If you are using react-navigation version v5 or newer you can use navigation.reset or CommonActions.reset:
 // Replace current navigation state with a new one,
 // index value will be the current active route:
navigation.reset({
  index: 0,
  routes: [{ name: 'Profile' }],
});
Source and more info here: https://reactnavigation.org/docs/navigation-prop/#reset
Or:
navigation.dispatch(
  CommonActions.reset({
    index: 1,
    routes: [
      { name: 'Home' },
      {
        name: 'Profile',
        params: { user: 'jane' },
      },
    ],
  })
);
Source and more info here: https://reactnavigation.org/docs/navigation-actions/#reset
For older versions of react-navigation:
v2-v4 use StackActions.reset(...)
import { StackActions, NavigationActions } from 'react-navigation';
const resetAction = StackActions.reset({
  index: 0, // <-- currect active route from actions array
  actions: [
    NavigationActions.navigate({ routeName: 'myRouteWithDisabledBackFunctionality' }),
  ],
});
this.props.navigation.dispatch(resetAction);
v1 use NavigationActions.reset
3) For android you will also have to disable the hardware back button using the BackHandler:
http://reactnative.dev/docs/backhandler.html
or if you want to use hooks:
https://github.com/react-native-community/hooks#usebackhandler
otherwise the app will close at android hardware back button press if navigation stack is empty.
Additional sources: thank you to the users that added comments below and helped keeping this answer updated for v5+.