Call an AngularJS function on button click is not working

You can not get filter values, because filter button is outside of controller and if you are using datatable then also add dt-option, dt-columns and dt-instance into <table> as attributes.

You have do like this way

<div ng-app="grdContrl" ng-controller="dtAssignVendor"> <!-- COMMON ANCESTOR-->
  <button class="btn btn-default customBtn" ng-click="GetFilter();">
    <i class="fa fa-filter" aria-hidden="true"></i> Filter
  </button>
  <div class="flTable" id="dtAssignVendor">
     <table id="assignVender" class="mp myTable table table-striped table-bordered" cellspacing="0" width="100%" datatable="" dt-options="dtOptions" dt-columns="dtColumns"  dt-instance="dtInstanceNonInvProduct">                            
     </table>
  </div>
</div>

Also inject into controller.

app2.controller('dtAssignVendor',function ($scope, $http, DTOptionsBuilder, DTColumnBuilder,DTInstances) {
       $scope.GetFiler = function () {
     //get input values into scope instead of javascript variable
    //var strZone = $('#SAPExecutive_R4GState').val();
    //var strUtility = $('#ddlUtility').val();
    $scope.strZone = $scope.SAPExecutive_R4GState;
    $scope.strUtility = $scope.ddlUtility;
    //redraw table on button click
    $scope.dtInstanceNonInvProduct.DataTable.draw();

}  
$scope.dtOptions = DTOptionsBuilder.newOptions().withOption('ajax', {
    url: AppConfig.PrefixURL + "/App/GetMPFilter",
    type: "POST",
    data: JSON.stringify({ strZone: $scope.strZone, strUtility: $scope.strUtility }),
})
.withPaginationType('full_numbers')
.withDisplayLength(10);
$scope.dtColumns = [
    DTColumnBuilder.newColumn(null, '').renderWith(function (data, type, full) {
        return '<input type="checkbox" class="check" data-object-id="' + full.objectid + '">'
    }),
    DTColumnBuilder.newColumn("MAINTENANCEZONENAME", "MAINTENANCEZONENAME"),
    DTColumnBuilder.newColumn("MAINTENANCEZONECODE", "MAINTENANCEZONECODE")
]

$scope.dtInstanceNonInvProduct = {};
})

The template of your code should be something like this:

<div ng-app="myApp">
    <div controller="ctrl1">
        <button ng-click="someFunInCtrl1()">Click Me</button>
        ...
    </div>
    <div controller="ctrl2">
        <button ng-click="someFunInCtrl2()">Click Me</button>
        ...
    </div>
</div>

You are unable to call GetFilter function because you are calling it from outside controller scope. As @Karim said

you need to use the ng-controller directive and wrap the button inside it

As far as i see you did not bind the controller to your template, you need to use the ng-controller directive and wrap the button inside it (and correct the spelling error on $scope.getFilter as raised in the comments)

<div ng-app="grdContrl" ng-controller="dtAssignVendor"> <!-- COMMON ANCESTOR-->
  <button class="btn btn-default customBtn" ng-click="GetFilter();">
    <i class="fa fa-filter" aria-hidden="true"></i> Filter
  </button>


 ---------------------------
  <div class="flTable" id="dtAssignVendor">
     <table id="assignVender" class="mp myTable table table-striped table-bordered" cellspacing="0" width="100%">                            
     </table>
  </div>
</div>