Is the goal to make a puzzle that when assembled is in the shape of a heart? If so, then just cut it. It doesn’t matter if you have pieces that extend beyond the outline of the heart; they’re scrap. There are several threads about making puzzles as evansd2 has pointed out.
If the goal to make a heart with a puzzle grid engraved on it? If so, then you can do the following or, just go for it like above. If you just go for it, it’ll take longer in the glowforge and you’ll have engraved scrap, but it’ll be done. The following is particularly useful when part of a larger piece. I’ll illustrate with a heptagon and a pattern of stars like so:
Step 1: Select all of the stars (puzzle pieces) and go to Object -> Group
Step 2: Select the single star object and go to Object -> Pattern -> Objects to Pattern.
Step 3: Select the heptagon (or heart), go to the Fill and Stroke menu, select Fill and select Pattern. This will fill the heptagon with your new pattern. If it doesn’t automatically select the pattern you just made, it’ll be in the drop down box with some name like pattern972.
At this point it is easy to think you have what you need. You’re wrong. If you upload this to your glowforge all you have is a heptagon (heart) to cut. Go back to the Fill and Stroke menu and select Stroke Paint - select none. The outline of the heptagon (heart) will disappear.
Step 4: Go to Edit -> Make a bitmap copy. You will now have an image (raster) over a vector. At this point you could go back to the Fill and Stroke menu, turn the stroke paint back on and upload to the GFUI. This should work because the glowforge will ignore the vector pattern. However, since this is something they will probably “fix” in the future, instead go to the Transform menu. and shift one of the two objects like so.
Step 5: Select the vector object and go to the Stroke and Fill menu. Change the Fill to none and turn the stroke paint back on. Then use the Transform menu and shift the heptagon (heart) back over the rasterized pattern. If uploaded to the glowforge, the blue line will want to cut and the stars will be engraved.
Note 1: You don’t have to move the raster in step 5. You could just turn the pattern off and the stroke paint back on. I did it to illustrate what needs to be done. Also, it can be difficult to tell what exactly is going on when you have objects directly over objects in Inkscape, especially for a noob.
Note 2: If you don’t set the stroke paint to None before you make the bitmap copy, the bitmap copy will include the outline of the heptagon (heart.) This is a rookie mistake (yup, I made it.) The glowforge engraves the outline and then it cuts it.