If you do not have access to another machine, you will have to get a bootable USB somehow, and use that.
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The following does involve turning on the machine, but *not* booting from the internal HDD. If that is a problem, you will have to take the HDD out and plug it into another machine. (You know — a PC (or Hackintosh) — with *actual* ports and slots and so on!!
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Later: Actually, I am thinking that your Mac might not have an optical drive. In that case, you will need to use “unetbootin” [for Linux or Mac, and presumably PC] to transfer the Clonezilla ISO onto a USB drive (again using another machine) [or, again, just use another machine for the whole thing]. [Read the notes at the end about 2GB limits; you can partition the USB stick into 1GB or less MBR, for the Linux, and the rest HFS+ (MacOS) for the image file.]
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If you have another machine, you can download Clonezilla, burn it onto a CD and boot from that. (It runs Linux; offhand, I am pretty sure that Macintoshes are happy to be treated as PCs.)
It is pretty straightforward if you are happy with disc partitions and [not blank terminal-type!] text interfaces; otherwise, it will probably look fairly daunting.
Clonezilla can copy <the partitions or the drive> directly onto another disc… or into an image file, to be restored onto the other disc as a separate procedure. Either way, you will have to have another hard disc, USB stick, optical disc (Blu-Ray) or whatever available. (Clonezilla can copy over a network, but I don’t know about that side of it.) The problem of course (I imagine) is that there is nowhere to plug a second HDD in directly. Probably the easiest way is to buy (or use!) an external drive adapter case with USB (AUD $25 to $50); you can then use Clonezilla to clone the internal drive onto the 2TB one (making sure that you allow it to resize the volume). [External drive adapters have maximum supported disc sizes; don’t buy a cheap one and find out that it can only handle 1TB.]
It is not *much* more difficult to make an image on a USB drive and then restore that. (You can run Clonezilla first to see how big the content is, without going through with the process; use the “ESC” key.)
• If you are using the image method: note that neither MBR nor FAT-32 can handle files more that 2GB (I am pretty sure); partition/format your image disc as GUID/MacOS (or NTFS (or possibly “ext4”)). You will then have to turn off Journalling — see below.
• It is okay to *read from* an HFS+ volume that has journalling. [To turn off journalling, you can use Disk Utility; unmount the disc, then use the Journalling item in the File menu.]
• Don’t change the keymappings.
• Make sure you include the boot partition (and any others) as well as the main volume.
• Note that the “d0s0” system starts with 0 but the “sda” system starts with 1.
