You can't. At least not officially. The steps outlined below are not recommended. They use part of the ArcGIS JS library that is not part of the public API and therefore this behavior may not work in the next version of the API or they may back-patch a previous version of the API and this could stop working even on something that previously did work.
That said, sometimes you need some "future" functionality right now and this is actually a pretty straightforward way of getting what you want using the common proxy pattern
Use the undocumented "private" function _getPrintDefinition
var proxy_getPrintDefinition = printTask._getPrintDefinition;
printTask._getPrintDefinition = function() {
var getPrintDefResult = proxy_getPrintDefinition.apply(this, arguments);
//Now you can do what you want with getPrintDefResults
//which should contain the Web_Map_as_JSON
console.log(Json.stringify(getPrintDefResult));
//make sure you return the result or you'll break this print task.
return getPrintDefResult;
}
_getPrintDefinition takes the map as the first argument and a PrintParameters object as the second.
so you'll have to create a PrintTask, redefine the _getPrintDefinition function on the newly created print task as outlined above, create a PrintParameters and then run:
myPrintTask._getPrintDefinition(myMap,myPrintParameters);
The results of this on my little test are:
{"mapOptions":{"showAttribution":false,"extent":{"xmin":-7967955.990468411,"ymin":5162705.099750506,"xmax":-7931266.216891576,"ymax":5184470.54355468,
"spatialReference":{"wkid":102100,"latestWkid":3857}},"spatialReference":{"wkid":102100,"latestWkid":3857}},
"operationalLayers":[
{"id":"layer0","title":"layer0","opacity":1,"minScale":591657527.591555,"maxScale":70.5310735,"url":"http://services.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/MapServer"},
{"id":"XXX-Redacted-XXX","title":"serviceTitle","opacity":1,"minScale":0,"maxScale":0,"token":"XXX-Redacted-XXX","url":"http://XXX-Redacted-XXX/arcgis/rest/services/TestService/MapServer"},
{"id":"XXX-Redacted-XXX","opacity":1,"minScale":0,"maxScale":0,"featureCollection":{"layers":[]}},
{"id":"featureGraphics","opacity":1,"minScale":0,"maxScale":0,"featureCollection":{"layers":[]}},
{"id":"map_graphics","opacity":1,"minScale":0,"maxScale":0,"featureCollection":{"layers":[]}}
]}
if you don't need to do any operations on the web map json and just need the output then you don't even need to use the proxy pattern.