The available evidence suggests:
- Drinking distilled water in usual amounts in everyday life, which includes regular meals, does not likely remove needed minerals from the human body in significant (harmful) amounts.
- Drinking large amounts of distilled water in a short time can result in water intoxication, but the danger is about the same as with tap water.
This topic is covered by two reviews of literature with the opposing results: one by World Health Organization and one by Water Quality Association.
A review by World Health Organization
A 2005 report by World Health Organization (WHO), Chapter 12: Health risks from drinking demineralized water
This review includes an earlier statement by WHO from 1980:
Salts are leached from the body under the influence of drinking water
with a low TDS. (TDS = total dissolved solids, which is basically mineral content.)
The author also says:
Results of experiments in human volunteers evaluated by researchers
for the WHO report are in agreement with those in animal experiments
and suggest the basic mechanism of the effects of water low in TDS
(e.g. < 100 mg/L) on water and mineral homeostasis. Low-mineral water
markedly: 1.) increased diuresis (almost by 20%, on average), body
water volume, and serum sodium concentrations, 2.) decreased serum
potassium concentration, and 3.) increased the elimination of sodium,
potassium, chloride, calcium and magnesium ions from the body.
In the above paragraph, there is a mixture of things that don't go together: the increase of both "body water volume" and "diuresis," and increase of both "serum sodium concentration" and "elimination of sodium."
My only explanation is that they mixed the results of various types of studies. For example, drinking usual amounts of distilled water (compared to isotonic beverages) increases diuresis, but not the "body water volume" (Nutrients, 2017; Table 3 and 4). On the other hand, drinking excessive amounts (several liters) of any water, not just distilled, in a short time (few hours) increases the "body water volume" (Stat Pearls, 2019). These are two totally different scenarios, so the results in the above review seem to be really mixed up.
Next, in the report, every water with less than 100 mg minerals per liter seems to be considered demineralized, while by definition, demineralized water contains less than 10 mg minerals per liter (EPA.gov). About 80 cities from a list of 100 big US cities have less than 100 mg/L of minerals in tap water, so does this mean that their tap water is harmful for health?
A review by Water Quality Association
A 1993 review by Water Quality Association: Consumption of low TDS water is basically a critic of the already mentioned statement by WHO from 198O (refered below as the "Soviet report") that salts are leached from the body under the influence of drinking water with a low TDS.
It has been concluded that the consumption of low TDS water, naturally
occurring or received from a treatment process, does not result in
harmful effects to the human body.
Several types of scientific literature searches have found no harmful
effects to the human body attributable to the consumption of low TDS
Review of the Soviet report has shown that the scientific methods used
are questionable and the conclusions are either vague or unsupported
by the data.
Many examples of real-world situations in which large populations have
been and continue to be provided exclusively with low TDS water
without any reported unusual or ill health effects, establishes the
safety of consuming such waters by human beings.
Can drinking distilled water result in water intoxication (dilutional hyponatremia)?
Only if you drink it in large amounts in a short time; it can occur with any water, not just distilled water. Distilled water has no sodium and has low osmolality (0 mmol/kg), but this is very similar to tap water which usually has <10 mg sodium/liter (Mgwater) and osmolality as low as 3 mmol/kg (SGSM.ch, Table 2). A woman has died after drinking ~6 liters of regular water in 3 hours (Scientific American). A bit more in detail on Medical SE.
Does drinking distilled water dehydrate you?
No, distilled water can hydrate you about as well as average tap water, because, as said, distilled and tap water may not be that different in mineral content and osmolality. In general, the hydration potential of a beverage increases with its sodium content (as explained in another answer).