How would I remove variables from a table?

How you remove elements from a table depends on how you inserted them. A table is a very general data structure that provides a mapping from any data type to any data type.

For example, you could have an array of players where integers are the keys and players are the values {[1] = player1, [2] = player2, etc..}. Or, you could have a dictionary where player names are the keys and player objects are the values {'Bob' = player1, 'ZetaReticuli' = player2, etc..}.

If you want to remove an object by key:

myTable[key] = nil --remove mapping of 'key' to its value in 'myTable'

If you want to remove an object by value:

function RemoveByValue(someTable, someValue)
    for key, value in pairs(someTable) do --iterate over keys and values
        if value = someValue then --find one that matches
            someTable[key] = nil --remove the key that maps to it
            break
        end
    end
end

Only use table.insert and table.remove when you are dealing with arrays - tables whose key values (indices) are integers (1, 2, 3, 4, etc...).

You can remove all of the objects in a table thus:

for key in pairs(someTable)
    someTable[key] = nil
end

If you would like further clarification please show how you insert objects into your survivor table.