Here's example code which lets you paint on the left side and which mirrors the canvas at runtime on the right side.
import java.util.Random;
import javafx.animation.AnimationTimer;
import javafx.application.Application;
import javafx.geometry.Point2D;
import javafx.scene.Node;
import javafx.scene.Scene;
import javafx.scene.SnapshotParameters;
import javafx.scene.canvas.Canvas;
import javafx.scene.canvas.GraphicsContext;
import javafx.scene.image.Image;
import javafx.scene.image.WritableImage;
import javafx.scene.input.MouseEvent;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.HBox;
import javafx.scene.paint.Color;
import javafx.scene.shape.Rectangle;
import javafx.stage.Stage;
public class Main extends Application {
    private static double SCENE_WIDTH = 1280;
    private static double SCENE_HEIGHT = 720;
    static Random random = new Random();
    Canvas canvas;
    Canvas copyCanvas;
    GraphicsContext graphicsContext;
    GraphicsContext copyGraphicsContext;
    AnimationTimer loop;
    Point2D mouseLocation = new Point2D( 0, 0);
    boolean mousePressed = false;
    Point2D prevMouseLocation = new Point2D( 0, 0);
    Scene scene;
    Image brush = createBrush( 30.0, Color.CHOCOLATE);
    double brushWidthHalf = brush.getWidth() / 2.0;
    double brushHeightHalf = brush.getHeight() / 2.0;
    @Override
    public void start(Stage primaryStage) {
        BorderPane root = new BorderPane();
        canvas = new Canvas( SCENE_WIDTH / 2, SCENE_HEIGHT);
        graphicsContext = canvas.getGraphicsContext2D();
        copyCanvas = new Canvas( SCENE_WIDTH / 2, SCENE_HEIGHT);
        copyGraphicsContext = canvas.getGraphicsContext2D();
        HBox hBox = new HBox();
        hBox.getChildren().addAll(canvas, copyCanvas);
        root.setCenter(hBox);
        scene = new Scene(root, SCENE_WIDTH, SCENE_HEIGHT);
        primaryStage.setScene(scene);
        primaryStage.show();
        addListeners();
        startAnimation();
    }
    private void startAnimation() {
        loop = new AnimationTimer() {
            @Override
            public void handle(long now) {
                if( mousePressed) {
                    // try this
                    // graphicsContext.drawImage( brush, mouseLocation.getX() - brushWidthHalf, mouseLocation.getY() - brushHeightHalf);
                    // then this
                    bresenhamLine( prevMouseLocation.getX(), prevMouseLocation.getY(), mouseLocation.getX(), mouseLocation.getY());
                }
                prevMouseLocation = new Point2D( mouseLocation.getX(), mouseLocation.getY());
                copyCanvas();
            }
        };
        loop.start();
    }
    private void copyCanvas() {
        SnapshotParameters params = new SnapshotParameters();
        params.setFill(Color.TRANSPARENT);         
        WritableImage image = canvas.snapshot(params, null);
        copyCanvas.getGraphicsContext2D().drawImage(image, 0, 0);
    }
    // https://de.wikipedia.org/wiki/Bresenham-Algorithmus
    private void bresenhamLine(double x0, double y0, double x1, double y1)
    {
      double dx =  Math.abs(x1-x0), sx = x0<x1 ? 1. : -1.;
      double dy = -Math.abs(y1-y0), sy = y0<y1 ? 1. : -1.;
      double err = dx+dy, e2; /* error value e_xy */
      while( true){
        graphicsContext.drawImage( brush, x0 - brushWidthHalf, y0 - brushHeightHalf);
        if (x0==x1 && y0==y1) break;
        e2 = 2.*err;
        if (e2 > dy) { err += dy; x0 += sx; } /* e_xy+e_x > 0 */
        if (e2 < dx) { err += dx; y0 += sy; } /* e_xy+e_y < 0 */
      }
    }
    private void addListeners() {
        scene.addEventFilter(MouseEvent.ANY, e -> {
            mouseLocation = new Point2D(e.getX(), e.getY());
            mousePressed = e.isPrimaryButtonDown();
        });
    }
    public static Image createImage(Node node) {
        WritableImage wi;
        SnapshotParameters parameters = new SnapshotParameters();
        parameters.setFill(Color.TRANSPARENT);
        int imageWidth = (int) node.getBoundsInLocal().getWidth();
        int imageHeight = (int) node.getBoundsInLocal().getHeight();
        wi = new WritableImage(imageWidth, imageHeight);
        node.snapshot(parameters, wi);
        return wi;
    }
    public static Image createBrush( double radius, Color color) {
        // create gradient image with given color
        Rectangle brush = new Rectangle(0,0,1,1);
        brush.setStroke(Color.RED);
        brush.setFill(Color.RED);
        // create image
        return createImage(brush);
    }
    public static void main(String[] args) {
        launch(args);
    }
}
Your code is in copyCanvas().

Tested with JavaFX 8u40, Win7. Although the antialiasing isn't as intense, the copy isn't a 1:1 copy. If you compare 2 lines on a pixel-level, you'll get this:

If you remove the 
params.setFill(Color.TRANSPARENT);  
you'll get a 1:1 copy: 

So it seems to have something to do with the transparent fill color in the SnapshotParameters.