How should a teaching-assistant calm his anxious student down in an exam?
I appreciate the gestures but I don't generally agree with the stated actions:


  I try to calm them down before the exam by talking to them privately
  after the class and reminding them that they are perfect students and
  should not allow nervousness to ruin their exam's mark


I would avoid doing that because it's borderline patronizing. It's impossible that all of them are perfect students and if you just talk to some of them who are nervous, that would not reflect well on the instructor from the angle of being objective and fair.


  At the exam hour, when I see such students; I try to bring them some
  water and sugar to help them feel more comfortable and answer their
  questions more relaxed.


Also awkward. By doing so you're singling out the seemingly nervous students. I don't oppose distributing some candies/snacks before hand but I don't agree with delivering food and drink to students who look like nervous.



Here are what I usually do to lower their anxiety:


Evaluate if examination is the best way of approaching the assessment, and if there are alternatives. Can the exam be distributed as three smaller tests? Weekly quizzes? Final project? I often use the students' likely career settings as a benchmark: Will they be more likely asked to write an analysis report with access to information, or trapped in a room to recite formula? etc.
Allow a one-page, self-prepared notes. It's a good compromise between closed-book and open-book. The actual benefit, however, happens when they were preparing for this piece of notes, as they have to actively digest and evaluate the information.
Incorporate questions that do have an absolute answer, but focus on showcasing thought process. Emphasize that there are some questions that have no absolute right or wrong answer, but merely to test the reasoning skills of the candidates.
Play some soothing classical music in the background prior to the start of the exam, and then fade it down before the starting time. Bach's work well... Vivaldi's four seasons work nicely as well.
Make some past questions available, or at least provide some mock example questions. This is to get rid of anxiety caused by unfamiliar format and types of questions.
Progress from basic, memory-based questions to more elaborated questions. Try not to strike too hard at the beginning. Build up their confidence through recalling some facts/definitions.
Clearly delineate the points allocated for each question. This is to ensure that they know they should stop before writing the 5th sentence for the 1/2 point.
Lower the proportion of final grade attributed to exams. Avoid having final exams bearing too much weight.
Invite seemingly collapsing students for a short break, and let them make up for the time afterwards. I have only done it once. The student was in serious distress: panting, red and teary eyes, heavy patches of sweat soaking through the shirt (room has AC.) I invited the student to go out for a chat, and the student immediately broke into loud crying once I closed the door. I and another TA gave the student some prep talk (aka, try your best, the past homework has shown that you can deal with the questions, etc.) and a 10-minute calm down. We let the student have 10 more minutes at the end. The student did manage to pass.