(Do NOT) Give up too quickly
Grad school can be a series of failures, which is OK. How do you expect to come up with something extraordinary, if you never ran into a dead end (or two)? You should not give up just because you failed once or twice. Just make sure you summarise what you’ve learned from each failure, so you don’t commit the same mistakes again and you are able build upon them next time. It’s up to YOU only, if/when there is a “next time”.
(Do NOT) Neglect your supervisor
The reason you have a supervisor, is because (s)he is meant to supervise you, regularly. If you have the right supervisor, you are a fool if you don’t take advantage of his/her support… and if you don’t have the right supervisor, then avoiding contact with the person will not solve anything, except postpone the “inevitable”. Bottom line: Either way, radio silence is definitely not a good idea.
(Do NOT) Isolate yourself
“No grad student is an island“. While in grad school, you should always be surrounded by people who nurture you. Be part of a group of grad school students who regularly (e.g. once a week) discuss their ongoing work. You will get valuable feedback and you will learn to see your own work differently, when you have to explain your progress to someone else.
(Do NOT) Waste Your Time
The importance of being able to say “NO” to BS is generally true in life, and grad school is no exception. If you want to graduate on time, decline everything that may delay your progress. If your supervisor regularly wants you to spend time on unskilled chores (e.g. administrative tasks, grading papers, you name it), then you may re-evaluate your options. It’s never too late to get out of a situation that’s clearly not working. Your goal is to graduate in a timely manner, so make sure you remove everything that goes against that goal.
… and there are certainly more common mistakes and limiting maxims you should avoid in graduate school, if you want to graduate on time.