Can a woman cut her hair and not cover her head? NIV 1 Corinthians 11:6 - For if a woman does not cover her head, she might
  as well have her hair cut off; but if it is a disgrace for a woman to
  have her hair cut off or her head shaved, then she should cover her
  head.


With reference to the context of this verse, 

Can a woman cut her hair (not shave her head) and not cover her head?

As she has two options, to cut her hair or shave her head. In verses, or is used as below:


  her hair cut off or her head shaved


She can opt any one of them(her hair cut off or head shaved), right?
No, the context does not state any such alternative that if she wishes to keep her hair uncovered then she may do that by keeping them short or shaving completely.  He is not suggesting an alternative between cutting hair or shaving bald; he says that for a woman to cut her hair short, or to shave bald, is very disgraceful.  Having short hair or shaved hair are both disgraceful  among Israelites of that period, although that is less disgraceful than displaying uncovered hair.  

Frederick Louis Godet's commentary says  


  To impress the revolting character of such a course, the
  apostle supposes it pushed to extremity. There is something of
  indignation in his words: “If this woman has effrontery enough to do
  the first of these acts, well and good, better also do the second!”
  The repulsive character of the one should make that of the other felt.
  The word ξυρασθαι is usually accented, as if it were the present
  infinitive passive of ξυράω (ξυρᾶσθαι). But why should it not be
  regarded as the aorist infinitive middle, like κείρασθαι, of the form
  ξύρω (ξύρασθαι)? See Passow. There is a gradation from the one of
  these verbs to the other: To cut the hair or even to shave the head.
  The word αἰσχρόν, shameful, includes the two notions of physical
  ugliness and moral indecency. (italics added)  


Charles Ellicott's commentary says


  (6) Let her also be shorn. —The force of this argument depends on the
  fact that a woman’s head being uncovered would be regarded by others
  as implying the same shame as was indicated by a woman’s hair being
  cut short (i.e., shorn), or altogether removed (i.e., shaven). It is
  as if the Apostle said —If a woman insists on her right to pray and
  speak in an assembly with uncovered head, let her carry out this
  principle to its logical result; let her insist on her right to have
  her hair cut short, so as to show her equality with man —and what would
  be thought of her then! No woman with a spark of shame in her would
  think of doing that. Accordingly you admit that this principle of
  sexual equality does not apply in all such matters; and it is
  illogical to argue in favour of any general principle as if it were of
  universal obligation, when you yourselves admit that it is not
  applicable in some cases.