Of course you don't need to save out to images and then reload to be able to work with sliced parts of an image. You can just skip all that save/load code and combine the two other code steps: slicing and doing something with each slice. Usually the pixel array is faster than get(), but get() can be more intuitive and a good solution at times as well.

How would I combine the two?  I dont understand how I would get the slice into the other part of the sketch without using slice.save and then reloading it.

Looking at your code above you first slice an image up into different small parts and then randomly put these together again. There are many ways to do that in Processing, without saving them to individual segments. Here is one example that does just that in a dynamic manner, so that you can move your mouse from left to right in order to determine the grid dimensions.

Also check out this thread for alternatives: https://forum.processing.org/topic/how-to-make-a-jigsaw

Code Example

1. PImage img = loadImage("http://www.hermitageshop.org/store/images/large/0003710A4_3_01_LRG.jpg");
2. float DIM;
3.  
4. void setup() {
5.   size(img.width, img.height, P2D);
6.   frameRate(10); // slowed down the frameRate, otherwise it's too fast to see
   
7.   noStroke();
8. }
9.  
10. void draw() {
11.   DIM = mouseX/10;
12.   float d = 1.0/DIM;
13.   beginShape(QUAD);
14.   texture(img);
15.   for (int y=0; y<DIM; y++) {
16.     for (int x=0; x<DIM; x++) {
17.       float cx = x/DIM;
18.       float cy = y/DIM;
19.       float nx = cx + d;
20.       float ny = cy + d;
21.       float tx = int(random(DIM)) / DIM;
22.       float ty = int(random(DIM)) / DIM;
23.       vertex(cx*width, cy*height, tx,   ty);
24.       vertex(nx*width, cy*height, tx+d, ty);
25.       vertex(nx*width, ny*height, tx+d, ty+d);
26.       vertex(cx*width, ny*height, tx,   ty+d);
27.     }
28.   }
29.   endShape();
30. }