Can I marry my maternal second cousin?

The third generation in the line of assent through the mother, and the fifth in the line of assent through the father, will come in Sapinda relationship. The line will start from the person concerned traced upward. The persons who are going to get married. As per the Hindu Marriage Act, 1955 restrict definition of Sapinda only up to the third generation of the mother.

In your case, your mother and her mother are granddaughters of a person. If you count the generations.

Ist generation is you and the girl whom you want to marry
2nd generation is your mother and her mother
3rd generation is Your maternal grandfather and her maternal grandfather are brothers. With this, the Sapinda relationship will end
4th generation is their father.
Your marriage will not come under Sapinda marriage of special marriage act,
You can go ahead and marry her. There is no controversy in this act.

Q: Can I marry my maternal second cousin?
A: As per the query raised and my understanding, I would say that, YES! you can marry your maternal second cousin and there is no illegality in that marriage.

Q: Does our relationship fall under SAPINDA category of Special Marriage Act?
A: The Sapinda relationship refers to relationship extending as far as the fifth generation in the line of the ascent of father and the third generation in the line of the ascent of the mother, where the generation includes you as the concerned person when tracking upward to be counted as the first generation.

As per Section 2(b) of Special Marriage Act, 1954, "A man and any of the persons mentioned in Part I and a woman and any of the persons mentioned in Part II of the First Schedule are within the degrees of prohibited relationship." In the clauses 3(f) and 3(g), the relationship includes -
a) Relationship by full blood or half or uterine blood
b) Illegitimate blood relationship as well as legitimate
c) Relationship by adoption as well as by blood

Full blood relationship - When two persons are related to each other from a common ancestor by the same wife they are said to be related to each other by full blood.
Half-blood relationship - When two persons are related to each other from a common ancestor but by the different wife they are said to be related to each other by half-blood.
Uterine blood relationship - When two persons are related to each other from a common ancestress but by the different husband they are said to be related to each other by uterine blood.
Here "ancestor" refers to father and "ancestress" refer to the mother

Q: Will our marriage be legally approved under Special Marriage Act?
A: Here, you are trying to marry your maternal second cousin which forms the third degree or generation of relation and also note that our law is liberal when it comes to customs and hence you can legally marry your maternal second cousin. Before taking your final decision, you need to speak to the elders of your family to get their approval and unite the families. In the later stage, do inform your doctor that your spouse is your maternal second cousin so as to avoid any complications in pregnancy.

As per section 5 of the Hindu Marriage act marrying in near cousins falling under Sapinda relationships are prohibited under the law. At the same time if it is as per the tradition of the particular community then in that case it is legally allowed. The law is very clear in the matter. The Sapinda relationship is defined in the law books as -

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The 'Sapinda' relationship with reference to any person extends as far as the third generation (inclusive) in the line of ascent through the mother, and the fifth (inclusive) in the line of ascent through the father, the line being traced upwards in each case from the person concerned, who is to be counted as the first.
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Keeping the above legislation in view you are outside the limit of Sapinda and go for this relationship. There are some health related aspects also which are considered by the people while going for cousin marriages but more and more you go away from first cousin to second and third the risks are reduced considerably.