Try below code:

    String.format("{0:MMM} {0:dd} {0:yyyy}",new Date(ows_Date)); 

In the `new Date()`function, pass the column name of the date field

Excellent reference - [Changing date format using javascript][1]

**Update** - you need to write a custom function as below:

    var monthNames = ["January", "February", "March", "April", "May", "June",
      "July", "August", "September", "October", "November", "December"
    ];
    
    function convertSPDate(d) {
    
        // split apart the date and time
        var xDate = d.split(" ")[0];
        var xTime = d.split(" ")[1];
    
        // split apart the hour, minute, & second
        var xTimeParts = xTime.split(":");
        var xHour = xTimeParts[0];
        var xMin = xTimeParts[1];
        var xSec = xTimeParts[2];
    
        // split apart the year, month, & day
        var xDateParts = xDate.split("-");
        var xYear = xDateParts[0];
        var xMonth = xDateParts[1];
        var xDay = xDateParts[2];
    
        var dDate = new Date(xYear, xMonth, xDay, xHour, xMin, xSec);
        return dDate;
    }

This will return the spservices column to a date object.

After that, you can use it as below:

    var convertedDate = convertSPDate($(this).attr("ows_Date"));
    
    var formattedDate = monthNames[convertedDate.getMonth()] + ' ' + convertedDate.getDate() + ' ' + convertedDate.getFullYear();

Modified from here - [jQuery function for formatting dates in SharePoint with SPServices][2]


  [1]: https://sharepoint.stackexchange.com/questions/160806/changing-date-format-using-javascript/160808#160808
  [2]: http://www.bentedder.com/jquery-function-for-formatting-dates-in-sharepoint-with-spservices/