You have several options for this journey. I can't say which is best for your specific case. I'm working on the assumption that you're leaving after work on a Friday and you need to be back for work on Monday morning.
It's a long drive, which means it will take most of a day, especially once you include breaks. If you're going down for a weekend, then you'll spend most of the Saturday travelling down and most of the Sunday travelling back, or possibly you can drive down on the Friday night and at least get all of Saturday together, though you'll arrive very late on Friday night (ie into Saturday morning). Also, you're likely to have to deal with very bad traffic getting around London (presumably on the M25), so your arrival time will be both unpredictable and liable to be delayed enough that you get too tired to complete the drive and need to stop off on the way (which means an expensive last-minute hotel/motel booking). Alternatively, you could have accommodation pre-booked (which should be cheaper) at a suitable spot to break the journey so you can arrive in Mullion earlier on the Saturday.
The only airport even faintly nearby is Newquay. Direct flights are only from Heathrow, which is not especially easy to get to from Braintree (you either have to drive all the way around London, or else take two trains and a tube). If you had more time, you might be able to use connecting flights and leave from Southend or Stratford (e.g. via Dublin), but that's not realistic for a weekend trip.
There is no reasonable way of getting from Newquay to Mullion other than by car - either hiring one, getting a taxi, or arranging for someone to give you a lift.
The closest station to Mullion is Redruth - and there's a bus (L1) from there to Mullion. But the bus doesn't run late at night, so you'd need to arrange transport from Redruth (book a taxi, perhaps). If you can catch the 5pm train from Braintree, then you can make the 19:04 from Paddington to Plymouth, and a change in Plymouth will get to you Redruth for 00:05 (five past midnight). If you can make it to Braintree station for 5pm, that seems like the only realistic way to get to Mullion the same night. Coming back, the last daytime train on a Sunday with connections to get you to Braintree would be the 16:44 from Redruth, and there's a bus leaving at 1453 from Mullion that will get you to Redruth for 1611, a reasonable connection.
There is a sleeper train between Paddington and Cornwall, which leaves Paddington at 2345 on Friday evening and arrives Redruth 0717. The first bus on a Saturday is at 0900 (arriving Mullion at 1013). Returning on the Sunday, the sleeper leaves Redruth at 2146 and reaches Paddington at 0504 on Monday morning, which should leave enough time to cross London and get to Braintree in time for work. The problem is that the last bus from Mullion to Redruth is the 1653, which would leave you waiting at Redruth station for nearly four hours (1806-2146), so you'd probably want to arrange alternative transport in the evening so you can spend more of Sunday with your girlfriend.
The bus timetables are here - train timetables are on the usual websites (e.g. National Rail).
All of these options are likely to be expensive - the daytime train is £130.60 (super off-peak return, which should cover any weekend train - you can get advance fares, but that ties you to a specific train); the sleeper is £55 extra each way if you want a bed (you can sleep in a seat if you want, but I wouldn't recommend that). Flights are about £135 return.