Here I'm talking about two minipcie ssd disks.
On a second thought, I think I can connect them simultaneously by simply removing wi-fi card from one of the slots.

Will check what Clonezilla is capable of.

Thanks for tips, Nick!

Clonezilla allows cloning via USB. Can you mount your new disk as a USB Disk? Also, remember, there is no need to be able to close up the case while doing the cloning. Most motherboards will have a spare SATA connector or two, and the PSU may have a spare power plug. You can get 1-to-2 power adaptors from fleabay. It does not need to be neat while cloning! In the past I've even put two PC's next to each other to take the power from one PC while the data went to the other PC. It is harder if you have a laptop as it won't have a spare SATA port so you are stuck with USB. Just one word of caution, cloning can be slow and can take quite a few hours.

Clonezilla also allows cloning to/from an image file which can be done by USB to an external drive. The external drive may have to be formatted as something other than FAT32 to avoid its 4GB file size limit.

Thanks Nick for the fast reply!

The problem is I have only one slot for hdd, so your way won't work in my case. I need to clone the system to an external hard drive and then set it up in a new internal disk.

As long as the new disk is the same size or larger, it is quite easy to do. The easiest way is to have both disks connected at the same time then boot of a Live Disk/USB of your choice and use the dd utility. I'd suggest something like Clonezilla which will boot of a USB pen. It has a bit of a GUI but I think it runs dd in the background. It has an option (in expert mode) to extend the last partition to use any spare space at the end of the disk as well, or you can boot into GParted and extend the partition afterwards. You may also be able to extend the partition from the command line in ClearOS, but I'm not sure if you can do it with the partition mounted.