Edit2: toLocaleFormat is not widely accepted. Here is a post on alternatives. You could just split it around the T. 
const dateArray = fullDateString.split('T');
if (dateArray.length > 0){
    const partYouWant = dateArray[0];
}
Edit: From the Ionic docs 
It's also important to note that neither the displayFormat or
  pickerFormat can set the datetime value's output, which is the value
  that is set by the component's ngModel. The format's are merely for
  displaying the value as text and the picker's interface, but the
  datetime's value is always persisted as a valid ISO 8601 datetime
  string.
Here is a better answer:
const dateObject = new Date(this.mydate);
const dateString = dateObject.toLocaleFormat('%Y-%m-%d');
An input for new Date can be a date string defined as:
String value representing a date. The string should be in a format
  recognized by the Date.parse() method (IETF-compliant RFC 2822
  timestamps and also a version of ISO8601).
I'm guessing you are trying to access this.mydate in your code.
You have several options, best represented by this stack overflow post. 
this.mydate.toLocaleFormat('%Y-%m-%d');
This function will take a Date object and convert it to the string in the format you requested. All the options you can put in the options are here. 
There are also plenty of other options shown in the stack overflow post above.