Have you simply tried to increase maximum memory available in Preferences?

Yes I have done that, simply works but slow.

" Maybe just like, if the Images are replaced by new one, the old one removed from screen? Or maybe preload the Images?"

Huh? How are you doing it already?

As tfguy44 points out, I think you might give more information about your program/code and purposes... It´d be easier to advice you then...
· Ale

I'm very new to this, but I had the same problem.

Indeed, if the images aren't too heavy, it can be one of the rare case where loading images in draw() is OK... You can also search for sketches loading images in a background thread, if you need to remain reactive while loading.

At first sight I think you could improve performance not resizing the pictures in draw(). Resize just after loading the image, thus you can save precious resources and you´ll avoid trying to re-resize an already resized picture...
bla,bla {
    mario[m] = loadImage("mario000"+m+".jpeg");
    mario[m].resize(imageWidth,imageHeight)
  }

Marginally, I think I wouldn´t call to width/2 and height/2 at any frame, load them both in variables (that´s not much important in this case, though)... Finally (and maybe most important), the fastest way to display a picture in screen is not background()... I think you should go into pixel arrays, that probably would be the simplest fast way of doing that (set() would be also better than background(), I think). You can try this also, although maybe it´s advanced stuff (and more interesting, for sure):
  https://forum.processing.org/topic/snippet-crazy-fast-image-loading
 
Good luck! :-)

Ale · 60rpm.tv/i

60rpm.tv emitted some good advices. I improve a bit your code with some of these and a bit more (untested):

1. // Variables for putting image sequences on screen.
2. int numPics = 100;
3.  
4. PImage[] mario = new PImage[numPics];
5.  
6. void setup() {
7.   size(800, 452);
8.   imageMode(CENTER);
9.  
10.   // Initializing the image sequences.
11.   for (int m = 0; m < mario.length; m++) {
12.     mario[m] = loadImage("mario" + nf(m, 3) + ".jpeg");
13.     mario[m].resize(width, height);
14.   }
15. }
16.  
17. void draw() {
18.   float i = int(map(mouseX, 0, width, 0, numPics));
19.   image(mario[i], width/2, height/2);
20. }

General advice: put numerical values in size(), it is useful if you export to an applet. And use the built-in variables instead.
Also I shown a trick with the nf() function simplifying a lot the loading code.

But there is no mystery: if you load lot of images, it will eat up load of memory...