It should still be food safe in the way you're probably thinking, but let me expand on a few ramifications.
The silicone, itself
If the manufacturer has fully complied with the requirements for labeling the item "food safe" (the safety of which is limited to using it for an intended purpose), the silicone, itself, should be food safe throughout. If you chop off a corner and expose the internal material, it won't transfer hazardous substances to your food.
The caveats to this part are:
You use it for the purpose it was approved for. There are many classes of food safe materials, and the requirements vary for usage characteristics such as temperature, incidental contact vs. long-term storage, the type of food it will be used with, etc. As long as you use the item for its advertised purpose, you're fine in this regard. For other purposes, it might or might not be fine. You don't know the limitations of the materials used and the manufacturer makes no claims, so you're on your own.
Food safety is generally defined by a government body of each country. Manufacturer's are expected to follow the guidelines and comply with the requirements of the countries in which the product will be sold. There generally isn't government oversight of the products manufactured. If a manufacturer labels something as food safe and it isn't, they could be subject to a private lawsuit, with the onus on the injured party to prove the problem. If a lot of people are injured by a product, or an issue that could threaten a lot of people happens to be identified, a government entity might order a recall or seize a shipment from another country.
Manufacturers of cheap products in certain countries have been known to cut corners as normal business practice. If the products are hazardous, and if the problem is identified, the penalty is usually just loss of the bad product. So there isn't a huge financial incentive to not cut corners. I'm not aware that food-safe silicone products from manufacturers in these countries have ever been a problem. But if you plan to modify such products and expose the interior material, that could potentially carry risks if the products aren't in compliance with their labeling. Just a consideration to think about when selecting products to modify.
In addition to the silicone, itself, there are food safety considerations related to the mechanical properties and condition of the food contact surface. If there are a lot of nooks and crannies, surface roughness, cracks, etc., those can be hard to clean and can harbor bacteria or contaminants. If you're going to modify a utensil or food mold, be careful to leave a smooth surface and no cracks, partial cuts, or seam openings.
Cutting out a feature on a mold
To remove a feature from a mold, you generally need to either fill it (if the feature is a protrusion on the finished item), or cut it out. Cutting something out of a mold generally leaves a hole, which then needs to be closed off. Either way, the materials you use for that will become part of the mold, so that also needs to be food safe.
It will need to bond sufficiently with the silicone in the mold to stand up to use as a mold, or at least be mechanically held in place during molding. So for that material, you need to consider not just whether it's food safe for this purpose, but whether it is suitable for a mold, and how you will ensure it maintains its shape without distortion, how you will incorporate it onto the silicone, etc.