Yes it is very easy to make tomato juice especially if you have a good food strainer, I have an old Victorio, all you do with it is core your tomatoes, quarter or half them put them in the hopper ontop, crank the handle and all the peels, seeds, and core are spit out a shoot and tomato pulp come's out another shoot, then you put it in a pot on the stove and heat it..I forget how long, at that point you can add anything you like for seasonings, etc. Then place in jars and water bath can.

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I hear this is really good.
Vegetable Juice Cocktail
2 tbls celery seed
7 quarts fresh tomatoes
2-3 peppers
3-4 onions
2 carrots
Lemon Juice
Salt
Sugar
Cook tomatoes. Liquify other vegetables in blender or food processor and add to tomatoes along with celery seed. (If you need to, you can add just a little cooked tomato mixture to the blender to help liquify. That's what I did) Simmer 45 minutes, put through a food mill, return to pan and bring back to a simmer. Pour hot into hot jars and to each pint jar add 1 tbls lemon juice, 1/2 tsp salt and 1/2 tsp sugar. Seal jars and pressure can 35 minutes at 10 pounds of pressure."

The reason the first recipe is pressure canned is due to the low acid veggies being added.

Makes about 7 quarts

Tomato Juice

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QUANTITY: An average of 23 pounds is needed per
canner load of 7 quarts, or an average of 14 pounds per
canner load of 9 pints. A bushel weighs 53 pounds and
yields 15 to 18 quarts of juice--an average of 3-1/4
pounds per quart.

PROCEDURE: Wash, remove stems, and trim off bruised
or discolored portions. To prevent juice from separating,
quickly cut about 1 pound of fruit into quarters and put
directly into saucepan. Heat immediately to boiling while
crushing. Continue to slowly add and crush freshly cut
tomato quarters to the boiling mixture. Make sure the
mixture boils constantly and vigorously while you add the
remaining tomatoes. Simmer 5 minutes after adding all
pieces.

IF YOU ARE NOT CONCERNED ABOUT JUICE SEPARATION,
simply slice or quarter tomatoes into a large saucepan.
Crush, heat, and simmer for 5 minutes before juicing.

Press both types of heated juice through a sieve or
food mill to remove skins and seeds. Acidify by adding
two tablespoons of bottled lemon juice or 1/2 teaspoon of
citric acid per quart of tomatoes. For pints, use one
tablespoon bottled lemon juice or 1/4 teaspoon citric
acid. Acid can be added directly to the jars before
filling with product. Add sugar to offset acid taste, if
desired. Four tablespoons of a 5 percent acidity vinegar
per quart may be used instead of lemon juice or citric
acid. However, vinegar may cause undesirable flavor
changes.

Heat juice again to boiling. Add 1 teaspoon of salt
per quart to the jars, if desired. Fill hot jars with hot
tomato juice, leaving 1/2-inch headspace. Adjust lids and
process.

RECOMMENDED PROCESS TIMES FOR TOMATO JUICE
IN A BOILING-WATER CANNER pints35 min. quarts 40 min.