Accessing a "Large" Table of Values in a Sketch?

A little background to my problem:

I have just built a very simple 2-axis CNC (PCB) mill that I would like to control with my arduino. The machine will only be used to cut very simple shapes, so I would like to avoid the whole CAD to GCode to GRBL toolchain altogether, simply writing a unique arduino sketch for each part containing all of the information necessary to mill it. Basically I will just insert two lists of numbers in my sketch that tell my cnc to move its x or y axis in a positive or negative direction. The machine will just cut basic "pixels" to form a shape based off the list of values I define in the sketch.

So what I am trying to accomplish is to put two lists of numbers in an arduino sketch (maybe anywhere fro 20 to 1000 integers depending on the shape to be milled and resolution). The value of a variable would change to the next number chronologically in the list each time a for loop is run. My first thought was to use simple arrays, but I found that an array can only store a maximum of 10 values before it begins accessing random memory locations, whereas I am talking about hundreds of numbers. My question is whether there is any way to make a large (10+ number) array, or if there is any other way altogether that I could store the necessary data within a sketch. Any suggestions would be awesome!

ogically in the list each time a for loop is run. My first thought was to use simple arrays, but I found that an array can only store a maximum of 10 values before it begins accessing random memory locations,

What? An array with 10 elements of Strings maybe, but not ints, chars, longs, shorts or bytes. Show me what lead you to this conclusion.

Yes an array can stor way more than 10 elements. The problem is that your array will normally be stored in SRAM and there is not so much of that.
You need to use program memory to store the array. Look that up in the referance section.

you should consider storing the numbers as a file on SD card.
Then you can prepare the numbers on a PC,
insert the SD in the arduino,
press start
Arduino reads numbers
execute the associated milling
Arduino reads numbers
execute the associated milling
Arduino reads numbers
execute the associated milling
Arduino reads numbers
execute the associated milling
Arduino reads numbers
execute the associated milling
Arduino reads numbers
execute the associated milling
etc
until EOF or some STOP command is encountered