Should a website be extremely slow when its running backups?
 

I have my own server and every night at 3:00am EST it runs a backup, and for about 15 minutes my sites are either down or extremely slow.
is this normal?

Not really...

What kind of processor and how much RAM do you have? Is this a server with a panel that offers a backup feature? Are there other cron jobs running at the same time? If you change the backup to a different time does it happen then too?

Depends how you are doing the backup... tar generally isn't well supported on most Linux kernels and will cause server load/slowdowns especially if you are tarring very large amounts of data, or directory structures with many subfolders and files.

Kernel tweaks or even an upgrade could help, check if you are swapping a lot during the process, changing to a hard drive with more RPM could also help...more RAM/CPU may have a minimal positive effect...

Personally, I'd use a combo of rsync+tar+gzip for backups.

... or get the backup software to run slower :)

yep, tar will eat you cpu time - my backup takes 12 hours to be done :(

Does this work like a home computer?
Linux lets you delegate tasks by core, right?
So just tell your backup program not to use the whole cpu...
Ought to bring your cpu AND disk usage down to an acceptable level