SpritesheetExamplePage.xaml

<Page
    x:Class="SpottedZebra.Examples.WinRT.SpritesheetExamplePage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d">

    <Grid Background="{StaticResource ApplicationPageBackgroundThemeBrush}">
        <Rectangle Width="100" Height="150">
            <Rectangle.Fill>
                <ImageBrush ImageSource="/Images/OwlSpritesheet.png" 
                            Stretch="None"
                            AlignmentX="Left" 
                            AlignmentY="Top">
                    <ImageBrush.Transform>
                        <TranslateTransform x:Name="SpriteSheetOffset" X="0" Y="0" />
                    </ImageBrush.Transform>
                </ImageBrush>
            </Rectangle.Fill>
        </Rectangle>
    </Grid>
</Page>

SpriteSheetExamplePage.xaml.cs

namespace SpottedZebra.Examples.WinRT
{
    using System;

    using Windows.UI.Xaml.Controls;
    using Windows.UI.Xaml.Media;
    using Windows.UI.Xaml.Navigation;

    public sealed partial class SpritesheetExamplePage : Page
    {
        private const int NumberOfColumns = 10;

        private const int NumberOfFrames = 51;

        private const int FrameWidth = 100;

        private const int FrameHeight = 150;

        public static readonly TimeSpan TimePerFrame = TimeSpan.FromSeconds(0.5);

        private int currentFrame;

        private TimeSpan timeTillNextFrame;

        public SpritesheetExamplePage()
        {
            this.InitializeComponent();
        }

        protected override void OnNavigatedTo(NavigationEventArgs e)
        {
            CompositionTarget.Rendering += this.OnUpdate;
        }

        protected override void OnNavigatedFrom(NavigationEventArgs e)
        {
            CompositionTarget.Rendering -= this.OnUpdate;
        }

        private void OnUpdate(object sender, object e)
        {
            this.timeTillNextFrame += TimeSpan.FromSeconds(1 / 60f);
            if (this.timeTillNextFrame > TimePerFrame)
            {
                this.currentFrame = (this.currentFrame + 1 + NumberOfFrames) % NumberOfFrames;
                var column = this.currentFrame % NumberOfColumns;
                var row = this.currentFrame / NumberOfColumns;

                this.SpriteSheetOffset.X = -column * FrameWidth;
                this.SpriteSheetOffset.Y = -row * FrameHeight;
            }
        }
    }
}

@geoffles, thank you. I struggled with this for a whole day.