I have a dual boot PC, with Ubuntu and Win 10. Can I install Mint without messing up GRUB or destroying the other OS?

The first issue is secure boot. I don't believe Mint supports secure boot so if it is enabled Mint won't install. Ubuntu does support secure boot.

Another important factor, are both Ubuntu and windows using UEFI? If so, then you need to install Mint UEFI. Best to have unallocated space available on which to install Mint and to know on which partitions you have Ubuntu and windows.

Simple answer, yes it is certainly possible but whether YOU can do it another question as we don't know your experience/knowledge on the subject. I'd definitely recommend reading a few of the many tutorials on dual booting Mint before beginning.

If both Ubuntu and Windows are using UEFI that means that the OP installed Ubuntu using UEFI so they already know that they need to install Mint in UEFI mode.

I don't know if you read the original post but the OP already has a dual boot Ubuntu and Windows system so they already have created a dual boot system. They are trying to create a triple boot system. What is the purpose of insulting the OP at this point and of your entire post.

That's an 'if' we don't have an answer to. Very likely that windows is uefi if pre-installed and also Ubuntu but we don't 'know' that. Both could be Legacy. It is also possible to mix but that requires accessing the BIOS to change the OS boot. Also, knowing it is necessary to install Mint uefi if the other systems are isn't the same as knowing how to do it. There are too many unknowns to be giving any specific advice and since the OP hasn't returned, hopefully s/he found some tutorials that helped out. Simple answer to the question asked is yes as I stated above and there is nothing insulting about my above post as we have no info on the knowledge of the OP.