Before you decide how to read a particular paper, you have to decide why you're reading that particular paper.
You said you're doing your Ph.D. You might want to take a look at a couple of other MO questions, such as When is one 'ready' to make original contributions to mathematics? and On starting graduate school and common pitfalls... and How to escape the inclination to be a universalist or: How to learn to stop worrying and do some research. If the reason you're reading these papers is that you think you have to absorb an infinite amount of mathematical knowledge before you can start doing research, then the first thing you need to do is: Stop thinking that.
One reason for reading a paper is that you have a specific research problem that you are trying to solve, and you believe that the paper contains a technique that will help you solve your problem. In such a situation, you should be constantly thinking, "Does this technique in fact help me solve my problem, and if so, how does the proof work?" If you determine that the paper does not help you solve your problem, I'd recommend abandoning ship, especially at this stage of your career. Your time is precious, and although mastering the techniques of the paper might come in handy one day, you have bigger fish to fry at the moment. On the other hand, if the paper does seem to solve your problem, then don't be afraid to sink a lot of time into it to understand it thoroughly. If some argument is logically needed for the proof of your own result, then you need to understand it completely, even if you end up just citing the other paper without reproducing the argument in your own paper.
Another reason for reading a paper is to increase your general store of mathematical knowledge. This is a laudable goal, but again, your time is precious. You first need to triage to decide how much effort to invest.
Option 0 is not to read it at all. This is what you will decide to do with most papers, because there are too many papers out there to even read the abstracts of all of them. If a paper is too far from your own area of work and looks like it will require significant effort to absorb, then drop it and move on.
Option 1 is to read just enough to get a general sense of what it is about, so that when you later run into a situation where you might need it, a bell will ring in your head ("Someone has done some relevant work on this") and you can return to the paper later. The important thing here is that even though you're not spending a lot of time on the paper, you should make some effort to put at least a "stub" of the paper in your long-term memory, so that when the occasion arises, the memory of this paper will be triggered. How you do this is up to you; maybe you can keep a log of some sort in which you write short notes to yourself about various papers you read, and re-read the log periodically to refresh your memory.
Option 2 is to read the paper more seriously, to understand in some detail what the results are, but stopping short of completely mastering the proofs. This is the sort of reading one tends to do when you're looking around for a new topic to work on, and think that this paper might be something you'll jump into and do research on yourself. You'll need to keep asking yourself, "Am I really going to work on this topic?" If you decide that the answer is no, then you should go to Option 1. If you decide that the answer is yes, then you may wish to proceed to Option 3 below.
Option 3 is to study the paper in full detail and master it. As I mentioned above, you should generally do this only when you're sure that understanding the proofs is needed to do your own research.
In short, the key is to triage, triage, triage. Decide as soon as you can why you are reading the paper and whether it is meeting your needs. Don't be afraid to drop the paper if it isn't meeting your needs, and don't be afraid of investing a lot of time into the paper if it is meeting your needs.