Corrupt Time Machine I have an external disk partitioned in three

/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *1.0 TB     disk1
   1:               Windows_NTFS Windows                 100.3 GB   disk1s1
   2:                  Apple_HFS Data                    400.1 GB   disk1s2
   3:                  Apple_HFS TimeMachine             499.7 GB   disk1s3


Now, the whole drive started to work bad: on the partitions that work, Windows and Data, to open a folder in Finder takes time, like ten secons to "list" what's inside. But TimeMachine doesn't work at all. It cannot be mounted by the system, so I can't access it.

Apart from that, once mounted (a weird thing is that I have to mount the partitions manually, before it automounted and the three partitions used to appear in the Desktop) I can't unmount them, nor eject the hard drive.

What can I do? Since I can access the data in Windows and Data, I can copy it (although it goes horribly slow) but what about TimeMachine, is there any way of accessing it if the system says it can't mount it?

I want to copy its contents and then format the whole drive to see if everything gets back to normal.

Any additional info needed, just ask.
This sounds like it could be a failing hardware component.  

Swap any connectors, try with a different cable, etc. IF this is a some major brand usb 3.0 external drives have internal usb 3.0 connectors fail frequently. Try it with a usb 2.0 micro cable and it may work fine at a slower speed.  If an external drive, you may be able to put into a drive dock to avoid issues with the factory housing and connectors.  

As soon as you get a stable connection, use the dd command, or something like daemon tools or 7 zip or whatever compression tool you prefer to dump the contents of each partition you don't want to lose to an iso to attempt recovery from later.  This is assuming you have another drive with sufficient capacity.  Let this complete before doing anything else so if the drive itself fails you have something to fall back to.

If you don't have any backup media, a clonezilla live cd could let you see the partition table really looks like and whether a filesystem to attempt to repair is still detected.

Consider the exFAT format for drives that need to walk in both worlds, and use a single hardware drive for TimeMachine if possible.  It has not worked well with multi partitioned drives in my experience, although it is a fantastic backup solution. 

Hope this helps!