There are no mantras in the Vedas (at least not in the portions that exist now) which explicitly state that the killer of a Cow should also be killed.
However, cows have been repeatedly mentioned as not to be be killed in Rig Veda mantras.
Cows should not be killed as per the Vedas
In RV 1.37.5, it's specifically stated, that cows should not be killed. The words used are
The word for killing in Vedas is "ghna". So, aghna means non-killing.
The word aghnayAh (not to be killed) or their variants also appear in many other mantras like RV 4.1.6, RV 1.164.27, RV 1.164.40 and there they refer to the Cows.
The word goghna (killing a Cow), on the other hand, occurs only once in the whole Rig Veda, namely in RV 1.114.10 which is a prayer to Lord Rudra not to harm the animals.
Cows are equated to the supreme Vedic deities like Indra in the Vedas
In Vedas the cows are indicated by words like gau or gavah, vasah (the barren cow), pashu.
Now, there are mantras in Rig Veda which equate Cows to Amrita (nectar of immortality). There are also mantras in the Vedas that equate Cows to the most prominent Vedic deities like Indra. I give below two such mantras:
VasAm Eva Amritam Ahuh, VasAm Mrityumupasate, Vasedam sarvamavad, DevA
ManushyA AsurAh Pitara Rishayah.
Vasha (the barren cow) they call as immortality (amrita), vasha they
worship (upAsate) as death, vasha became all this (sarvam abhavat),
Gods, men, asuras, fathers and rishis.
GAvo Bhago, GAvo Indro, Ma IcchAd GAvah Somasya Prathamasya Bhakshah.
To me the Cows (gavah) are Bhaga, they are Indra, they are a portion
of the first poured Soma.
However, in Smritis there are verses which say that we should even give up our lives in order to save the Cows. So, these verses indicate (and encourage) us in engaging in some form of combat to save Cows from being killed.
Manu Smriti 10.62. Dying, without the expectation of a reward, for the
sake of Brahmanas and of cows, or in the defence of women and
children, secures beatitude to those excluded (from the Aryan
Manu Smriti 11.79. He who unhesitatingly abandons life for the sake of
Brahmanas or of cows, is freed from (the guilt of) the murder of a
Brahmana, and (so is he) who saves (the life of) a cow, or of a
- When spectators keep aloof, and refrain from giving help to cows or bulls in distress they are affected by sin. (Parashara Smriti).
So, these verses are likely to be the ones which might have encouraged the organization to say whatever they have said.
But, in Vedas there are no such explicit orders. But as i have said, Vedas also clearly mention that Cows should not be killed.
RV 4.21.5-------> Rig Veda Mandala 4, Sukta 21, Mantra 5 etc.