The old time cut 'n suck method of snake bite treatment came about before it was understood that not all bites carried venom and how quickly venom can be absorbed by surrounding tissue. Secondary infections caused by cutting open of the wound area and/or bacteria from hands or saliva of the one administering first aid often became more serious.
There are sites that caution against using the suction cup type of first aid, along with the cut 'n suck method made famous in old westerns. I have tried to link a couple of them (see below the quote) but I am not sure if the link will work (let me know if they don't). I am not sure there is any definitive word on this device though most sites I looked through have language similar to what NCCE says below, there are no measurable advantages in its use.
From the NC Cooperative Extension - Snake Bite First Aid publication
ACTIONS TO AVOID:
DO NOT cut the bite. The additional tissue damage may actually increase the diffusion of the toxins throughout the body.
DO NOT apply a tourniquet. Such action can result in the loss of the limb.
NEVER try to suck out the venom by mouth. You can try the suction cup in a snakebite kit if it doesn't delay other needed treatment. Suctioning seldom provides any measurable advantages, however.
Do not apply cold and/or ice packs. Recent studies indicate that application of cold or ice makes the injury much worse.
The recommended treatments presented are those published in the current edition of Brady's Emergency Care for the Sick and Injured, the standard training and procedures manual for Emergency Medical Technicians.
http://Snake bite First Aid - What do you do?
http://Treat a Snakebite - Backpacker