Commentary for Deuteronomy 14:1

לא תתגדדו YE SHALL NOT CUT YOURSELVES — i.e. you shall not make cuttings and incisions in your flesh for the dead in the way the Amorites do (Sifrei Devarim 96:11), because you are children of the Lord and it is therefore becoming for you to be comely and not cut about and with hair torn out.

YE ARE THE CHILDREN OF THE ETERNAL YOUR G-D: YE SHALL NOT CUT YOURSELVES, NOR MAKE ANY BALDNESS BETWEEN YOUR EYES FOR THE DEAD. This also is an explanatory commandment of what He said in the Torah with reference to the priests, They shall not make baldness upon their head etc., nor make any cuttings in their flesh,¹⁹²Leviticus 21:5. and now he [Moses] will explain that it is not merely because of the distinction of the priests which He mentioned there, They shall be holy unto their G-d,¹⁹³Ibid., Verse 6. that they were thus commanded. Rather, all the congregation are holy, every one of them,¹⁹⁴Numbers 16:3. and all of you are the children of the Eternal your G-d like the priests; if so, you too, take heed to yourselves regarding this commandment like them. This explanation is in accordance with the opinion of our Rabbis¹⁹⁵Yebamoth 13b. that both verses [the one here and the one in Leviticus] relate only to the practice [of cutting and making baldness as signs of mourning] for the dead, [although “the dead” is not mentioned in the priestly injunction in Leviticus]. But it is possible that the first commandment [in Leviticus was stated] in relation to priests to state that if the priest had his hair torn out and his flesh cut, he was not fit for the Divine Service, just as He said, and they shall not profane the Name of their G-d,¹⁹³Ibid., Verse 6. and their Service is thus profaned [i.e., invalidated]. Here he explained that the commandment applies also to the Israelites, both prohibitions being necessary.¹⁹⁶By combining both statements we deduce that the prohibition against making baldness relates to the whole head and not only between the eyes, that it relates to the practice in connection with mourning for the dead, and finally that a separate penalty is incurred for each incision into the flesh (Makkoth 20 a-b).
And Rashi wrote: “Because you are the children of the Eternal it is becoming for you to be comely and not be cut about and bald [due to the tearing out of hair].” But it is not correct, for if so this commandment should be binding even [if the deeds were done] not for the dead! And Rabbi Abraham ibn Ezra commented: “Once you realize that you are the children of the Eternal and that He loves you more than a father loves his child, you should not cut yourselves [in bereavement] for anything that He does, because whatever He has done is for your good although you may not understand it, just as little children do not understand their father, yet rely on him. For thou art a holy people,¹⁹⁷Verse 2. and you are not like all the other nations; therefore you shall not do as they do.”
In my opinion the purport of the expression for thou art a holy people¹⁹⁷Verse 2. [is to state] an assurance of the eternal existence of the souls before Him, blessed be He. The verse declares: “Since you are a holy people and the treasure of G-d — neither doth G-d respect any person, but He deviseth means that he that is banished be not an outcast from Him¹⁹⁸II Samuel 14:14. — therefore it is improper for you to make incisions in your flesh and tear your hair for the dead even if he perisheth in youth.¹⁹⁹Job 36:14. Scripture, however, did not prohibit weeping for the dead since it is natural to cry when parting from beloved ones, and when they go on a journey even in life. From this verse, there is support for our Rabbis in prohibiting excessive mourning for the dead.²⁰⁰Moed Katan 27b.

בנים אתם לה' אלוקיכם, לא תתגודדו, it is bad manners to display excessive grief over the loss of a relative as long as a more relevant relative (G’d) is still alive. This is why G’d reminds us in this context that we are His children, i.e. that whatever relative we may mourn we have a father who is alive and well so that we are not really orphaned.