Does “Alternate page with proper canonical tag” hurt SEO?

Not when these are pages that intentionally point elsewhere: parameter, filter and sort variants, print versions. It's only a problem if the list includes a page that should have its own place in results.

How do I remove a page from this report?

If the page should be indexed on its own, give it a self-referencing canonical and make sure its content isn't a copy of another page. Then request indexing in the URL Inspection tool.

Why is the number of pages in this report growing?

Usually because of new parameter URLs (filters, campaign tracking) that Google discovers in links. Growth alone isn't a problem as long as the canonical points to the right pages.

Alternate page with proper canonical tag

Usually not an error. Google found a page whose canonical tag points to another URL, agreed with that choice and indexed the canonical page instead. You only need to act if the list contains a page that should rank on its own.

What this status means

The page has a <link rel="canonical"> pointing to another URL. Google read the hint, agreed with it, and indexed the canonical page rather than this one. In the Search Console Pages report these URLs sit under "Not indexed", but that group is informational — not every entry is an error.

When it's fine

parameter URLs such as ?sort=price, ?color=black or ?utm_source=… pointing to the clean URL,
print versions, AMP or separate mobile pages pointing to the main version,
pagination or product variants deliberately consolidated into one canonical page.

In these cases everything works as designed and there's nothing to do.

When you need to act

Check whether the list includes pages that used to bring traffic or should rank on their own — categories, products, articles.

Typical causes of a wrong canonical:

a template or plugin adds a canonical to the homepage or a category on every page,
after a migration, canonicals point to old URLs or to http instead of https,
the canonical points to a URL that redirects or returns 404 — check it with the redirect checker.

How to fix it

Open the page and check where rel="canonical" points in the source.
If the page should be in results, set the canonical to its own URL.
Make sure the content isn't nearly identical to another page — otherwise Google may still pick that one.
In Search Console, use URL Inspection and request indexing.

How not to miss it next time

A wrong canonical usually arrives with a deployment and works silently. IndexRise compares the canonical of every monitored page with the baseline. When it starts pointing to another URL, you get a critical "Page is no longer indexable" event with the URL it points to.