In theory, this CAN kill you, but it would be incredibly painful and take a long time, as well as leave you with long-term vascular dysfunction in the event that you survive (which is, by the way, very likely). You'd need to target multiple major vessels at once in order to get the best results, and some of them are in pretty difficult spots to get to.
First off, the water is not heated to the body's internal temperature, which will cause sudden cooling of your blood vessels and, eventually, it will also make its way to your heart. This will cause arrhythmia and it will cause the area you injected the water into to stiffen up and tighten. Your blood will thicken, resulting in hypoxia, leading to slow and drawn out cell death in that area, akin to frostbite.
Second off, assuming that you go through with this and inject a large amount of water into several of your key veins, this will cause a reaction called hemolysis, which causes your blood cells to violently burst open. You'll enter shock and most likely fall unconscious, but not before suffering involuntary spasms, uncontrollable shivering and intense chest pain. When you do wake up, which is likely, you'll have suffered permanent damage.
For best results, you'd have to rapidly inject a lot of water-- at least a liter to be safe, I'd reckon-- into multiple veins that are close to your heart, like your subclavian and inferior vena cava, in order to attack your heart from multiple angles simultaneously, hoping that this will induce cardiac arrest. The problem is that your body is prepared for this, and your blood will rapidly clot and thicken in response, to prevent any of the water from reaching your vital organs. So, realistically, you'd have to try and cause severe clotting in almost every cardiovascular pathway. Not very easy.
In a nutshell, this won't work unless you are strapped down to a table and someone else does it for you, and even then, you'll have an agonizing death.