Purification through bittul renews vitality

אא"ז ז"ל הגיד בפרשת פרה שמטהר מטומאת מת והוא הסתלקות חיות הפנימיות והעצה להיות בטל כעפר ואפר אל חיות השי"ת.

My grandfather, of blessed memory, said regarding Parashas Parah, that it purifies from the tumah (impurity) of [contact with] a corpse — which is the departure of the inner life-force — and the counsel [for this] is to be nullified like dust and ash before the life-force of Hashem.

The Chiddushei HaRim taught that the Parah Adumah purifies from corpse-impurity, which represents the withdrawal of inner vitality. The remedy is bittul: making oneself like the parah's "dust and ash," utterly nullified before Hashem's living force.

ועל ידי זה מתחדש החיות.

And through this the life-force is renewed.

By nullifying oneself to Hashem in this way, fresh vitality flows in and the lost inner life is renewed.

ולכך פ' החודש אח"כ.

And therefore Parashas HaChodesh [is read] afterward.

Because Parah brings renewal of vitality, it is fittingly followed by Parashas HaChodesh — the parashah of renewal (chodesh from chadash) — which expresses the very hischadshus that the purification produces.

עכ"ד פח"ח:

These are his words — and how pleasant are the words of the wise (pikchin chiddushin / "pleasant are these words").

The Sefas Emes closes by attributing the teaching to his grandfather, marking it as a beautiful insight.

Summary: The Chiddushei HaRim taught that Parah Adumah purifies from corpse-impurity, which represents the departure of inner vitality. The remedy is bittul — nullifying oneself like dust and ash before Hashem's life-force — through which one's vitality is renewed. This is why Parashas HaChodesh, the parashah of renewal, follows Parashas Parah.