If you would like to scrape the security code off the back of the card, there is nothing stopping you. However, it may hurt the usability of the card, and you won't be gaining as much security as you might think.
The purpose of the security code has been discussed in another question, but basically, it is there to prove that you have the physical card in your hand in cases where it is uncertain that you do. When you are at a physical store and scan your card at a Point of Service (POS) terminal, either by magnetic strip or by chip, you don't need the security code. However, if the scan fails and the clerk needs to type in your number, the POS terminal will generally ask for the security code to prove that the physical card is present. If the clerk can't read the security code, you'll need to provide it. If you are in a situation where you aren't there with the clerk at the terminal (a restaurant setting, for example), this will result in a delay.
Removing the security code does provide a security benefit, but only in two specific circumstances that I can think of:
- If your card is physically stolen.
- If a store clerk writes down your card number while temporarily in possession of your card.
In the first instance, once your card is physically stolen, you will report it, and you will be on the lookout for fraudulent transactions. The fact that the security code is not present on the card is only of minimal benefit, because the thief can still use the card at a physical store, until the card is deactivated. You will not ultimately be held responsible for any fraudulent transactions.
In the second instance, this security measure could be of use, but again, you won't ultimately be held responsible for any fraudulent transactions.
Neither of these types of fraud are the most common. Instead, much more common is cases where your card number is obtained either by skimming or by hacking. Scraping off the security code will not stop either of these.