>>11906058They are in the same way related to veins and arteries in the sense that they are different conducts that transport fluids along the body of the plant and do so in different flows.
But that's where the similitudes ends, now it's been quite a while since I studied it but what I remember clearly is that xylemn is actually a dead tissue, it does not pump anything anywhere and phloem activelly pumps sugars along the plant with it's companion cells(that are even devoid of nucleus). So, if you also notice that plants do not have hearths like animals, the reason why water flows within the plant is a mix of radicular pressure and transpiration.
Radicular pressure it's pretty much osmotic pressure coming from the roots, the different concentrations of sugars and other molecules with the environment pushes water into the root and this creates enough pressure to push the water to the top of the plant. But is very limited and only works in certain plants when they are young. In fact, you can see it precisely in the way you described: One humid morning cut the stem of a young plant and you will notice that it will start slowly acumulating and dropping fluids on top, but not many and not for long and I will explain later
But transpiration is the real engine of fluids in plants. You can consider a plant a giant hollow tube that connects the humid ground with the wet air, so it forces the water of the ground to go through itself to reach the air creating pressure, actually very strong pressure.
Now, have in mind that both of those fluids aren't a continuous tube either(another difference with animal conducts) but rather a series of tubes connected with holes, that are designed to keep and direct the flow(so it doesn't go backwards) and to collapse in case of damage, so if you were do what you describe, unless it was a very clean cut, most of the tubes would collapse and block themselves stopping the flow.