Can't see external HDD partition in Disk Utility
David's answer already explains what probably happened to your drive. You accidentally partitioned the drive instead of erasing just a volume.

According to your statement your drive contained two partitions previously:


First partition: 280 GB
Second partition: 1720 GB


After repartitioning the drive only one partition is left:


First and only partition: 228.4 GB


This probably means that the second partition wasn't affected - only the entry in the MBR was removed.

You should be able to recover the partition by simply adding a second partition in the MBR.

To detect the former boundaries of the lost partition you have to search for specific strings on the disk which determine the first and last block of a (former) NTFS volume.

The specific strings are either NTFS or BOOTMGR/bootmgr. 

The content of the block depends on your locale, so searching for "BOOTMGR is compressed" (found in an English NTFS Partition Boot Sector) is not necessarily successful. "BOOTMGR" (English/German) or "bootmgr" (Spanish/French?) should work though. I haven't tested non-latin Windows systems.

Examples 

First block of a German NTFS volume:



Last block of a German NTFS volume:



This can be done by dd'ing the device to grep.

Example:

$ sudo dd if=/dev/disk2 bs=512 skip=2048 count=512 | grep -o -a -b "BOOTMGR"    
421:BOOTMGR
512+0 records in
512+0 records out
262144 bytes transferred in 0.010566 secs (24810155 bytes/sec)


The explanation of the command:

Copy /dev/disk2 with a block size of 512 Byte to stdout, but skip the first 2048 blocks of disk2 and stop after (another) 512 blocks, pipe it to grep, treat the output as text, search for "BOOTMGR" and finally show the byte offset(s) of the matched pattern in front of the respective matched line.

In your case the result 71010552671:BOOTMGR of sudo dd if=/dev/disk2 bs=512 skip=446333006 count=150000000 | grep -o -a -b "BOOTMGR"means:

The byte offset is 71010552671 Byte after the last block (block 446333006) of the currently existing HDD1 volume on disk1. In blocks that's the relative block 138692486 or the absolute block (446333006 + 138692486) = 585025492.

This means two things:


Your previous partition 1 probably had a size of ~ 299 GB (= ~278 GiB) instead of 280 GB
Your partitions aren't aligned properly to 4k blocks because neither 446333006 nor 585025492 are divisible by 8




The last block of the vanished NTFS volume can be expected in the last 10,000 blocks of disk2. The appropriate command to search for it is then

sudo dd if=/dev/disk2 bs=512 skip=3907019167 count=10000 | grep -o -a -b "BOOTMGR"


With the result of the command you can determine the last block of the vanished partition 2.

With the first block and the last block you can add the lost partition with fdisk to the MBR.

To crosscheck the size you can extract the partition size in sectors in the partition boot sector at offset 0x028 and field length of 8 Bytes and the sector size at offset 0x0B and field length of 2 Bytes.

In the example screenshots above that's FF E7 DF E8 00 00 00 00 (= 3906988031+1) and 00 02 (= 512 Byte).

The diskutil info output for the example volume (visible in the screenshots) is:

...
Disk Size:                2.0 TB (2000377872384 Bytes) (exactly 3906988032 512-Byte-Units)
Device Block Size:        512 Bytes
...