Just get all documents and save them to file e.g.:

from bson.json_util import dumps
from pymongo import MongoClient

if __name__ == '__main__':
    client = MongoClient()
    db = client.db_name
    collection = db.collection_name
    cursor = collection.find({})
    with open('collection.json', 'w') as file:
        file.write('[')
        for document in cursor:
            file.write(dumps(document))
            file.write(',')
        file.write(']')

The accepted solution produces an invalid JSON. It results in trailing comma , before the close square bracket ]. The JSON spec does not allow trailing commas. See this answer and this reference.

To build on the accepted solution I used the following:

from bson.json_util import dumps
from pymongo import MongoClient
import json

if __name__ == '__main__':
    client = MongoClient()
    db = client.db_name
    collection = db.collection_name
    cursor = collection.find({})
    with open('collection.json', 'w') as file:
        json.dump(json.loads(dumps(cursor)), file)

Here's another way of not saving a , before the closing square brackets. Also using with open to save some space.

filter = {"type": "something"}
type_documents = db['cluster'].find(filter)
type_documents_count = db['cluster'].count_documents(filter)

with open("type_documents.json", "w") as file:
    file.write('[')
    # Start from one as type_documents_count also starts from 1.
    for i, document in enumerate(type_documents, 1):
        file.write(json.dumps(document, default=str))
        if i != type_documents_count:
            file.write(',')
    file.write(']')

It basically doesn't write the comma if number of iterations is equal to the number of documents (which is the last document it saves).